# Applying Ratios in Right Triangles

ID: zugis-hovos
Illustrative Mathematics, CC BY 4.0
Subject: Geometry

13 questions

# Applying Ratios in Right Triangles

Classroom:
Due:
Student Name:
Date Submitted:
##### Problem 1

1) Mai is visiting Paris to see the Eiffel Tower. She is 80 feet away when she spots it. To see the top, she has to look up at an angle of 85.7 degrees. How tall is the Eiffel Tower? Round your answer to the nearest whole foot.

##### Problem 2

Find the missing measurements of the right triangle.

2) Find the measure of angle ﻿$B$﻿.

3) Find the length of side ﻿$AB$﻿. Round your answer to the nearest tenth of a unit.

4) Find the length of side ﻿$AC$﻿. Round your answer to the nearest tenth of a unit.

##### Problem 3

5) Gateway Arch in St. Louis, Missouri, is 630 feet tall. Priya can look up at a 50 degree angle to see the top of the arch. How far away from the base of the arch is she standing? Round your answer to the nearest whole foot.

##### Problem 4

6) Based on the figure, which equation is true?

a)

﻿$\sin$﻿(32﻿$\degree$﻿)=﻿$\frac{8.5}{x}$﻿

b)

﻿$\sin$﻿(32﻿$\degree$﻿)=﻿$\frac{x}{8.5}$﻿

c)

﻿$\cos$﻿(32﻿$\degree$﻿)=﻿$\frac{8.5}{x}$﻿

d)

﻿$\cos$﻿(32﻿$\degree$﻿)=﻿$\frac{x}{8.5}$﻿

##### Problem 5

7) Kiran is flying a kite. He gets tired, so he stakes the kite into the ground. The kite is on a string that is 12 feet long and makes a 45 degree angle with the ground. How high is the kite?

a)

12 ft

b)

﻿$\frac{12}{\sqrt{2}}$﻿ ft

c)

12﻿$\sqrt{2}$﻿ ft

d)

24 ft

##### Problem 6

Match each of the ratios with one of the angle measures listed below.

Angle measures: ﻿$14\degree$﻿, ﻿$28\degree$﻿, ﻿$47\degree$﻿, ﻿$58\degree$﻿, ﻿$82\degree$﻿

8) adjacent leg ﻿$\div$﻿ hypotenuse = 0.139

9) opposite leg ﻿$\div$﻿ adjacent leg = 0.249

10) opposite leg ﻿$\div$﻿ hypotenuse = 0.469

11) adjacent leg ﻿$\div$﻿ hypotenuse = 0.682

12) opposite leg ﻿$\div$﻿ hypotenuse = 0.848

##### Problem 7

13) In the right triangles shown, the measure of angle ﻿$ABC$﻿ is the same as the measure of angle ﻿$EBD$﻿.​​ What is the length of side ﻿$BE$﻿?