Question

The angle of elevation to the top of a 30-story skyscraper is measured to be 4° from a point on the ground 2,500 feet from the building. What is the height of the skyscraper to the nearest hundredth foot?

A: 174.82 feet
B: 174.39 feet
C: 83.13 feet
D: 96.49 feet

A 50-foot tree casts a shadow 9 feet long. The sine of the angle of elevation of the top of the tree to the sun is approximately______.

A: 0.01
B: 0.18
C: 0.02
D: 0.98

Which of the following triangles are right triangles? Check all that apply.

A triangle with side lengths 6 inches, 8 inches, 10 inches,

A triangle with side lengths 5, 12, 13

A triangle with side lengths 9, 12, 15

A triangle with side lengths 8, 15, 17

Answer 1

Answer on Question #57979 – Math – Trigonometry

Question

The angle of elevation to the top of a 30-story skyscraper is measured to be $4{}^{\circ}$ from a point on the ground 2,500 feet from the building. What is the height of the skyscraper to the nearest hundredth foot?

A: 174.82 feet

B: 174.39 feet

C: 83.13 feet

D: 96.49 feet

Solution

We have a right triangle, where

b is the height of the skyscraper, $a = 2,500$ feet and $A = 4{}^{\circ}$. Then $b/a = \tan A$; $b = a \tan A$; $b = 2.500 \cdot \tan 4{}^{\circ} \approx 174.82$

Answer: A.

Question

A 50-foot tree casts a shadow 9 feet long. The sine of the angle of elevation of the top of the tree to the sun is approximately

A: 0.01

B: 0.18

C: 0.02

D: 0.98

Solution

We have a right triangle,

$b = 50$ feet, $a = 9$ feet, then by Pythagorean Theorem, $c = \sqrt{2500 + 81} \approx 50.80354$. We have to find $\sin B = a/c$; $\sin B = 9/50.80354 \approx 0.18$.

Answer: B. 0.18

Question

Which of the following triangles are right triangles? Check all that apply.

A triangle with side lengths 6 inches, 8 inches, 10 inches,

A triangle with side lengths 5, 12, 13

A triangle with side lengths 9, 12, 15

A triangle with side lengths 8, 15, 17

Solution

Using the Pythagorean theorem, $a^2 + b^2 = c^2$, check

$$\sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10;$$ $$\sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13;$$ $$\sqrt{9^{2} + 12^{2}} = \sqrt{81 + 144} = \sqrt{225} = 15;$$ $$\sqrt{8^{2} + 15^{2}} = \sqrt{64 + 225} = \sqrt{289} = 17.$$

Answer: All these triangles are right.

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