Triangles: Pythagorean Theorem & Special Triangles

Triangles: Pythagorean Theorem & Special Triangles

Special right triangles(45-45-90 and 30-60-90)

Pythagorean Theorem:a2 + b2 = c2

Special Pythagorean Triples: (3, 4, 5), (6, 8, 10), (5, 12, 13), (8, 15, 17)

(from TAKS Information Booklet - Exit level - sample items)

1.The cable cars of a ski lift rise 5,000 vertical feet from the base at a constant 30o angle of inclination.

What is the approximate straight-line distance that a cable car travels from the base to the summit of the mountain?

A.2,500 ft

B.2,900 ft

C.8,500 ft

D.10,000 ft

2. Mr. Ryan is flying his single-engine plane at an altitude of 2400 feet.

He sees a cornfield at an angle of depression of 30o.

What is Mr. Ryan's approximate horizontal distance from the cornfield at this point?

A.1200 ft

B.3394 ft

C.4157 ft

D.4800 ft

3.If A andB are complementary angles and mA is x, which equation can be used to find y, mB?

A.y = 90 + x

B.y = 90 - x

C.y = 180 - x

D.y = x + 180

4.A fence around a square garden has a perimeter of 48 feet. Find the approximate length of the diagonal of this square garden.

A.12 ft

B.17 ft

C.21 ft

D.24 ft

5.A ramp used for skateboarding rises from the ground at a 30° angle. If the ramp covers 20 ft on the ground, about how long is inclined surface of the ramp?

A.10.0 ft

B.11.55 ft

C.23.09 ft

D.40.0 ft

6.A ladder is propped against a building so that it forms it forms a 60o angle with the ground. If the ladder is 20 feet long, what is the distance d in feet from the ground to the point on the side of the building where the ladder rests? Round your answer to the nearest hundredth.

x = ______

8. x = ______

Find the perimeter of each object. Give exact answers.

______10.

______9.

______11.

______12.