How to find an angle in a right triangle - Geometry
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A right triangle has side lengths of 5, 10, and 11.18 inches. One angle is 63.4 degrees. What is the measure of the other angle?
A right triangle has side lengths of 5, 10, and 11.18 inches. One angle is 63.4 degrees. What is the measure of the other angle?
Since this is a right triangle, simply add this right angle to the given angle and subtract from 180 degrees.
The side lengths are not relevant in this problem.
Since this is a right triangle, simply add this right angle to the given angle and subtract from 180 degrees.
The side lengths are not relevant in this problem.
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Find the degree measure of the missing angle.
Find the degree measure of the missing angle.
All the angles in a triangle add up to 180º.
To find the value of the remaining angle, subtract the known angles from 180º:
Therefore, the third angle measures 43º.
All the angles in a triangle add up to 180º.
To find the value of the remaining angle, subtract the known angles from 180º:
Therefore, the third angle measures 43º.
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Find angle C.
Find angle C.
First, know that all the angles in a triangle add up to 180 degrees.
Each triangle has 3 angles. Thus, we have the sum of three angles as shown:
where we have angles A, B, and C. In our right triangle, one angle is 25 degree and we'll call that angle A. The other known angle is 90 degrees and we'll call this angle B. Thus, we have
Simplify and solve for C.
First, know that all the angles in a triangle add up to 180 degrees.
Each triangle has 3 angles. Thus, we have the sum of three angles as shown:
where we have angles A, B, and C. In our right triangle, one angle is 25 degree and we'll call that angle A. The other known angle is 90 degrees and we'll call this angle B. Thus, we have
Simplify and solve for C.
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Which of the following can be two angle measures of a right triangle?
Which of the following can be two angle measures of a right triangle?
A right triangle cannot have an obtuse angle; this eliminates the choice of 100 and 10.
The acute angles of a right triangle must total 90 degrees. Three choices can be eliminated by this criterion:
The remaining choice is correct: 
A right triangle cannot have an obtuse angle; this eliminates the choice of 100 and 10.
The acute angles of a right triangle must total 90 degrees. Three choices can be eliminated by this criterion:
The remaining choice is correct:
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A right triangle has an angle that is 15 more than twice the other. What is the smaller angle?
A right triangle has an angle that is 15 more than twice the other. What is the smaller angle?
The sum of the angles in a triangle is 180. A right triangle has one angle of 90. Thus, the sum of the other two angles will be 90.
Let 
= first angle and 
= second angle
So the equation to solve becomes 
or 
Thus, the first angle is 
and the second angle is 
.
So the smaller angle is 
The sum of the angles in a triangle is 180. A right triangle has one angle of 90. Thus, the sum of the other two angles will be 90.
Let
So the equation to solve becomes
Thus, the first angle is
So the smaller angle is
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What is the missing angle in this right triangle?
What is the missing angle in this right triangle?
The angles of a triangle all add up to 
.
This means that 
.
Using the fact that 90 is half of 180, we can figure out that the missing angle, x, plus 34 adds to the remaining 90, and we can just subtract
.
The angles of a triangle all add up to
This means that
Using the fact that 90 is half of 180, we can figure out that the missing angle, x, plus 34 adds to the remaining 90, and we can just subtract
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Angle 
in the triangle shown below (not to scale) is 35 degrees. What is angle 
?
Angle
The interior angles of a triangle always add up to 180 degrees. We are given angle 
and since this is indicated to be a right triangle we know angle 
is equal to 90 degrees. Thus we know 2 of the 3 and can determine the third angle.
Angle 
is equal to 55 degrees.
The interior angles of a triangle always add up to 180 degrees. We are given angle
Angle
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Which of the following cannot be true of a right triangle?
Which of the following cannot be true of a right triangle?
All of these statements are false.
A right triangle can be equilateral.
False: An equilateral triangle must have three angles that measure 
each.
One leg can be longer than the hypotenuse.
False: Each leg is shorter than the hypotenuse.
A right triangle can have an obtuse angle.
False: Both angles of a right triangle that are not right must be acute.
The measures of the angles of a right triangle can total 
.
False: The measures of any triangle total 
.
All of these statements are false.
A right triangle can be equilateral.
False: An equilateral triangle must have three angles that measure
One leg can be longer than the hypotenuse.
False: Each leg is shorter than the hypotenuse.
A right triangle can have an obtuse angle.
False: Both angles of a right triangle that are not right must be acute.
The measures of the angles of a right triangle can total
False: The measures of any triangle total
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In triangle 
, what is the measure of angle 
?
In triangle
The formula to find all the angles of a triangle is:
To solve for the measure of angle 
, we plug in the values of 
and 
. Since angle 
is a right angle, we know the measure will be 
.
The formula to find all the angles of a triangle is:
To solve for the measure of angle
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The right triangle 
has two equal angles, what is each of their measures?
The right triangle
The internal angles of a triangle always add up to 180 degrees, and it was given that the triangle was right, meaning that one of the angles measures 90 degrees.
This leaves 90 degrees to split evenly between the two remaining angles as was shown in the question.
Therefore, each of the two equal angles has a measure of 45 degrees.
The internal angles of a triangle always add up to 180 degrees, and it was given that the triangle was right, meaning that one of the angles measures 90 degrees.
This leaves 90 degrees to split evenly between the two remaining angles as was shown in the question.
Therefore, each of the two equal angles has a measure of 45 degrees.
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Solve for 
:
Solve for
The angles of a triangle add together to 180 degrees. We already know that one of the angles is 90 degrees, so we can subtract 90 from 180: the other 2 angles have to add to 90 degrees.
We can now subtract to get x:
The angles of a triangle add together to 180 degrees. We already know that one of the angles is 90 degrees, so we can subtract 90 from 180: the other 2 angles have to add to 90 degrees.
We can now subtract to get x:
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Determine the missing angle in this right triangle:
Determine the missing angle in this right triangle:
The angles of a triangle always add to 180 degrees.
That means that in this case,
since we know that the right angle is 90 degrees.
There are a few ways we can move on from here, but one is to simplify this equation:
now subtract 145
The angles of a triangle always add to 180 degrees.
That means that in this case,
There are a few ways we can move on from here, but one is to simplify this equation:
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A right triangle has equal legs of 
, and a hypotenuse of 
. Find the area.
A right triangle has equal legs of
The equation to find the area of a triangle is:
In this problem, both the base and the height are 6in. By plugging in the numbers, we get
The equation to find the area of a triangle is:
In this problem, both the base and the height are 6in. By plugging in the numbers, we get
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Find the measurement of 
.
Find the measurement of
Recall that the angles inside of a triangle must add up to 
. The small square in the corner of the triangle indicates that it is a right angle that measures 
degrees.
Thus, for the triangle in question,
Recall that the angles inside of a triangle must add up to
Thus, for the triangle in question,
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Find the measurement of 
.
Find the measurement of
Recall that the angles inside of a triangle must add up to 
. The small square in the corner of the triangle indicates that it is a right angle that measures 
degrees.
Thus, for the triangle in question,
Recall that the angles inside of a triangle must add up to
Thus, for the triangle in question,
Compare your answer with the correct one above
Find the measurement of 
.
Find the measurement of
Recall that the angles inside of a triangle must add up to 
. The small square in the corner of the triangle indicates that it is a right angle that measures 
degrees.
Thus, for the triangle in question,
Recall that the angles inside of a triangle must add up to
Thus, for the triangle in question,
Compare your answer with the correct one above
Find the measurement of 
.
Find the measurement of
Recall that the angles inside of a triangle must add up to 
. The small square in the corner of the triangle indicates that it is a right angle that measures 
degrees.
Thus, for the triangle in question,
Recall that the angles inside of a triangle must add up to
Thus, for the triangle in question,
Compare your answer with the correct one above
Find the measurement of 
.
Find the measurement of
Recall that the angles inside of a triangle must add up to 
. The small square in the corner of the triangle indicates that it is a right angle that measures 
degrees.
Thus, for the triangle in question,
Recall that the angles inside of a triangle must add up to
Thus, for the triangle in question,
Compare your answer with the correct one above
Find the measurement of 
.
Find the measurement of
Recall that the angles inside of a triangle must add up to 
. The small square in the corner of the triangle indicates that it is a right angle that measures 
degrees.
Thus, for the triangle in question,
Recall that the angles inside of a triangle must add up to
Thus, for the triangle in question,
Compare your answer with the correct one above
Find the measurement of 
.
Find the measurement of
Recall that the angles inside of a triangle must add up to 
. The small square in the corner of the triangle indicates that it is a right angle that measures 
degrees.
Thus, for the triangle in question,
Recall that the angles inside of a triangle must add up to
Thus, for the triangle in question,
Compare your answer with the correct one above