Intermediate Geometry : How to find an angle in an acute / obtuse triangle

Example Questions

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Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

In ΔABC, A = 75°, a = 13, and b = 6.

Find B (to the nearest tenth).

30.4°

27.8°

28.1°

26.5°

34.9°

26.5°

Explanation:

This problem requires us to use either the Law of Sines or the Law of Cosines. To figure out which one we should use, let's write down all the information we have in this format:

A = 75°       a = 13

B = ?          b = 6

C = ?          c = ?

Now we can easily see that we have a complete pair, A and a. This tells us that we can use the Law of Sines. (We use the Law of Cosines when we do not have a complete pair).

Law of Sines:

To solve for b, we can use the first two terms which gives us:

Example Question #5 : How To Find An Angle In An Acute / Obtuse Triangle

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is . The measure of angle CBD is . The length of segment is 4.

Find the measure of .

Explanation:

The measure of  is . Since , , and  are collinear, and the measure of  is , we know that the measure of  is .

Because the measures of the three angles in a triangle must add up to , and two of the angles in triangle  are  and , the third angle, , is .

Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle

The largest angle in an obtuse scalene triangle is  degrees. The second largest angle in the triangle is  the measurement of the largest angle. What is the measurement of the smallest angle in the obtuse scalene triangle?

Explanation:

Since this is a scalene triangle, all of the interior angles will have different measures. However, it's fundemental to note that in any triangle the sum of the measurements of the three interior angles must equal  degrees.

The largest angle is equal to  degrees and second interior angle must equal:

Therefore, the final angle must equal:

Example Question #3 : How To Find An Angle In An Acute / Obtuse Triangle

In an obtuse isosceles triangle the largest angle is  degrees. Find the measurement of one of the two equivalent interior angles.

Explanation:

An obtuse isosceles triangle has one obtuse interior angle and two equivalent acute interior angles. Since the sum total of the interior angles of every triangle must equal  degrees, the solution is:

Example Question #4 : How To Find An Angle In An Acute / Obtuse Triangle

In an acute scalene triangle the measurement of the interior angles range from  degrees to  degrees. Find the measurement of the median interior angle.

Explanation:

Acute scalene triangles must have three different acute interior angles--which always have a sum of  degrees.

Thus, the solution is:

Example Question #5 : How To Find An Angle In An Acute / Obtuse Triangle

The largest angle in an obtuse scalene triangle is  degrees. The smallest interior angle is  the measurement of the largest interior angle. Find the measurement of the third interior angle.

Explanation:

An obtuse scalene triangle must have one obtuse interior angle and two acute angles.

Therefore the solution is:

All triangles have three interior angles with a sum total of  degrees.

Thus,

Example Question #6 : How To Find An Angle In An Acute / Obtuse Triangle

The largest angle in an obtuse isosceles triangle is  degrees. Find the measurement for one of the equivalent acute interior angles.

Explanation:

An obtuse isosceles triangle has one obtuse interior angle and two equivalent acute interior angles. Since the sum total of the interior angles of every triangle must equal  degrees, the solution is:

Example Question #7 : How To Find An Angle In An Acute / Obtuse Triangle

In an acute isosceles triangle the largest interior angle is  degrees. Find the measure for one of the two equivalent acute interior angles.

Explanation:

The sum of the three interior angles in any triangle must equal  degrees. Therefore, the solution is:

Example Question #8 : How To Find An Angle In An Acute / Obtuse Triangle

Find the value of .

Explanation:

To find the value of , consider the fundamental notion that the sum of the three interior angles of any triangle must equal  degrees.

Thus, the solution is:

Example Question #9 : How To Find An Angle In An Acute / Obtuse Triangle

An obtuse isosceles triangle has an interior angle with a measure of  degrees.

Select the answer choice that displays the correct measurements for the two other interior angles of the triangle.

,

Explanation:

An obtuse isosceles triangle has one obtuse interior angle and two equivalent acute interior angles. Since the sum total of the interior angles of every triangle must equal  degrees, the solution is:

Therefore, each of the two equivalent interior angles must have a measurement of  degrees each.

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