Acute / Obtuse Triangles

Help Questions

ACT Math › Acute / Obtuse Triangles

Questions 1 - 10

_tri11

What is the value of in the triangle above? Round to the nearest hundredth.

Cannot be calculated

Explanation

Begin by filling in the missing angle for your triangle. Since a triangle has a total of degrees, you know that the missing angle is:

Draw out the figure:

_tri12

Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:

$\frac{sin(30)}{30}=\frac{sin(100)}{x}$

Solving for , you get:

$x=\frac{30sin(100)}{sin(30)}=59.0884651807326...$

Rounding, this is .

_tri11

What is the value of in the triangle above? Round to the nearest hundredth.

Cannot be calculated

Explanation

Begin by filling in the missing angle for your triangle. Since a triangle has a total of degrees, you know that the missing angle is:

Draw out the figure:

_tri12

Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:

$\frac{sin(30)}{30}=\frac{sin(100)}{x}$

Solving for , you get:

$x=\frac{30sin(100)}{sin(30)}=59.0884651807326...$

Rounding, this is .

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

$60^{\circ}$

$20^{\circ}$

$90^{\circ}$

$45^{\circ}$

$75^{\circ}$

Explanation

Since the sum of the angles of a triangle is $180^{\circ}$ , and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:

$x+3x+5x=180$

$9x=180$

$x=20$

If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.

_tri61

What is the value of in the triangle above? Round to the nearest hundredth.

Cannot be computed

Explanation

What is the value of in the triangle above? Round to the nearest hundredth.

Begin by filling in the missing angle for your triangle. Since a triangle has a total of degrees, you know that the missing angle is:

Draw out the figure:

_tri62

Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:

$\frac{sin(34)}{17}=\frac{sin(135)}{x}$

Solving for , you get:

$x=\frac{34sin(135)}{sin(34)}=42.99344718275794$

Rounding, this is .

_tri61

What is the value of in the triangle above? Round to the nearest hundredth.

Cannot be computed

Explanation

What is the value of in the triangle above? Round to the nearest hundredth.

Begin by filling in the missing angle for your triangle. Since a triangle has a total of degrees, you know that the missing angle is:

Draw out the figure:

_tri62

Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:

$\frac{sin(34)}{17}=\frac{sin(135)}{x}$

Solving for , you get:

$x=\frac{34sin(135)}{sin(34)}=42.99344718275794$

Rounding, this is .

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

$60^{\circ}$

$20^{\circ}$

$90^{\circ}$

$45^{\circ}$

$75^{\circ}$

Explanation

$x+3x+5x=180$

$9x=180$

$x=20$

If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.

_tri21

What is the value of in the triangle above? Round to the nearest hundredth.

Cannot be computed

Explanation

Begin by filling in the missing angle for your triangle. Since a triangle has a total of degrees, you know that the missing angle is:

Draw out the figure:

_tri22

Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:

$\frac{sin(20)}{7}=\frac{sin(50)}{x}$

Solving for , you get:

$x=\frac{7sin(50)}{sin(20)}=15.67834879458227...$

Rounding, this is .

_tri21

What is the value of in the triangle above? Round to the nearest hundredth.

Cannot be computed

Explanation

Begin by filling in the missing angle for your triangle. Since a triangle has a total of degrees, you know that the missing angle is:

Draw out the figure:

_tri22

Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:

$\frac{sin(20)}{7}=\frac{sin(50)}{x}$

Solving for , you get:

$x=\frac{7sin(50)}{sin(20)}=15.67834879458227...$

Rounding, this is .

There are two similar triangles. One has side lengths of 14, 17, and 19. The smaller triangle's smallest side length is 2. What is the length of its longest side?

Explanation

Use proportions to solve for the missing side:

$\frac{2}{14}=\frac{x}{19}$

Cross multiply and solve:

$\frac{38}{14}=x=2.7$

_tri31

What is the length of side ? Round to the nearest hundredth.

Cannot be computed

Explanation

Begin by filling in the missing angle for your triangle. Since a triangle has a total of degrees, you know that the missing angle is:

Draw out the figure:

_tri32

This problem becomes incredibly easy! This is an isosceles triangle. Therefore, you know that is , because it is "across" from a degree angle—which matches the other degree angle!

Page 1 of 5

Return to subject