Lesson 6E More Than Right Develop Understanding

Ready

Find the area of each triangle.

1.

Triangle EFG with angle F 45 degrees, FG=5radical2 cm and FE 14 cm.

2.

Triangle ABC with BC = 18 cm and AC = 38 cm

3.

Triangle ABC with Angle A is 60 degrees; AB = 14 cm and AC = 11 cm.

4.

Isosceles Triangle PQR. Angle P is 70 degrees and PR = 16 cm.

5.

Triangle GHK with angle G with 30 degrees and GK=24 ft

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.

Two right triangles share the same side, d. The base of one triangle is x mi and the other 6 miles more than the smaller one.

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.

Triangle with top vertex labeled Ben's Hideout, Left vertex; Star Point = 34 degrees; right vertex: Twin Pines = 14. Base is 30 mi. Ben's HideoutTwin PinesStar Point

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.

11.

Right triangle with one angle 45 degrees and hypotenuse 16 in.

12.

Isosceles right triangle with hypotenuse 34 ft.

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 .

14.

Right triangle with one angle 60 degrees and opposite side 15 cm.

15.

Right triangle with one angle 60 degrees and opposite side 24 m.

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.

17.

Right triangle with one angle 45 degrees and opposite side s.

18.

Right triangle with one angle 30 degrees and hypotenuse H.

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

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