# Lesson 10Finding the Value of a RelationshipSolidify Understanding

For each story presented, sketch a picture of the situation and label as much of the picture as possible.

### 1.

Jill put a ladder up against the house to try to reach a light that is out and needs to be changed. She knows the ladder is long, and the distance from the base of the house to the bottom of the ladder is .

### 2.

Francis is flying an airplane at an altitude of , when he begins a descent toward the ground. The plane has an angle of descent that is .

### 3.

Abby is standing at the top of a very tall skyscraper and looking through a telescope at the scenery all around her. The angle of decline on the telescope says , and Abby knows she is floors up and each floor is tall.

## Set

For problems 4–7, use the sketches you made in problems 1–3, or make new sketches, to help you find the missing values.

### 4.

Jill put a ladder up against the house to try to reach a light that is out and needs to be changed. She knows the ladder is long and the distance from the base of the house to the bottom of the ladder is . How high does the ladder reach up on the side of the house? What is the angle of elevation formed by the ladder and the ground?

### 5.

Francis is flying an airplane at an altitude of , when he begins a descent toward the ground. If the angle of descent of the plane is , how far will the plane travel through the air before it is on the ground?

### 6.

Abby is standing at the top of a very tall skyscraper and looking through a telescope at the scenery all around her. The angle of decline on the telescope says , and Abby knows she is floors up and each floor is tall. How far from the base of the building is the object that Abby is looking at?

### 7.

A -tall person is standing away from a skyscraper looking up at the top of the building and wondering how tall the skyscraper is. The angle of elevation for the person’s line of sight is . Determine the height of the building.

## Go

Use the given right triangle to identify the trigonometric ratios and angles.

, ,

, ,

, ,

, ,

,

, ,

, ,

, ,

### 11.

Place a point on that splits the segment into two segments with lengths that have a ratio of . Provide the coordinates of the point.

### 12.

Draw a segment on the grid and place a point on the segment to split it into two segments with lengths that have a ratio of .