# Lesson 6EMore Than RightDevelop Understanding

Find the area of each triangle.

## Set

Solve the following application problems using right triangle trigonometry.

### 6.

Students in a high school mathematics class were given the following problem.

While traveling across a flat stretch of desert, Joey and Holly make note of the top of a butte* in the distance that seems to be directly in front of them. They estimate the angle of elevation to the top as . After traveling miles towards the butte, the angle of elevation is . Approximate the height of the butte in miles and in feet. . Use the given values to solve for in miles and in both miles and feet. and

* Buttes are tall, flat-topped, steep-sided towers of rock.

### 7.

Rework problem 6. This time use . Or, use the values in your calculator without rounding them.

### 8.

The situation in problem 6 included approximating angles, so rounding didn’t matter very much. Consider a situation where Joey and Holly were serious rock climbers and were planning on scaling the face of the butte, and they had used an inclinometer* to measure the angles of elevation accurately. Describe the difference between rounding to one decimal place and rounding to four or more decimals.

* An inclinometer is an instrument used for measuring angles of slope, elevation, or depression of an object with respect to a plane.

### 9.

The Star Point Ranger Station and the Twin Pines Ranger Station are apart along a straight, mountain road. Each station gets word of a cabin fire in a remote area known as Ben’s Hideout. A straight path from Star Point to the fire makes an angle of with the road, while a straight path from Twin Pines makes an angle of with the road. Find the distance, , of the fire from the road.

### 10.

In problem 9 we had two expressions that were both equal to . Use both of your expressions and the value you found for in problem 7 to check your answers.

Explain why they were not exactly equal. Does it matter if this application were real life? Why or why not?

## Go

Solve for the missing sides and angles in the right triangles. Write answers in radical form. Do NOT use a calculator.

### 13.

Write a rule for finding the sides of an isosceles right triangle when you know the hypotenuse and the measure of the hypotenuse does NOT show a .

### 16.

Write a rule for finding the missing sides in a triangle when you know the side opposite the angle, but the measurement doesn’t show a .

Fill in the missing measurements.

### 18.

Fill in the ratios for the given functions. Do not use a calculator. Answers should be in radical form.

### 19.

 $\mathrm{sin}45°=$ $\mathrm{cos}45°=$ $\mathrm{tan}45°=$

### 20.

 $\mathrm{sin}30°=$ $\mathrm{cos}30°=$ $\mathrm{tan}30°=$

### 21.

 $\mathrm{sin}60°=$ $\mathrm{cos}60°=$ $\mathrm{tan}60°=$