Question

Fill in the blank.

The light from a lamppost casts a shadow of a man who is standing 15 feet away from the lamppost. The man's shadow is 5 feet long. The angle of elevation from the tip of the shadow to the lamp is 50 degrees. To the nearest foot, the lamppost is ______ feet tall.

The Pythagorean theorem is true for all similar triangles
A: true
B: False

Answer 1

Answer on Question #57924 - Math - Trigonometry

Task 1. Fill in the blank.

The light from a lamppost casts a shadow of a man who is standing 15 feet away from the lamppost. The man's shadow is 5 feet long. The angle of elevation from the tip of the shadow to the lamp is 50 degrees. To the nearest foot, the lamppost is ______ feet tall.

Solution.

$AB$ - the lamppost;

$CD$ - the man;

$CF$ - the shadow of the man;

So, $AC = 15$ feet, $CE = 5$ feet, $\angle AEB = 50{}^{\circ}$ .

$AE = AC + CE = 15 + 5 = 20$ feet.

$ABE$ - a right triangle.

Using the definition of Tangent:

$$\tan \angle A E B = \frac {A B}{A E}$$

Therefore:

$$A B = A E \cdot \tan \angle A E B$$

So,

$AB = 50 \cdot \tan 50{}^{\circ} \approx 59.59 \approx 60$ feet.

Answer: 60 feet.

Task 2. The Pythagorean theorem is true for all similar triangles

A: True

B: False

Solution.

We can use the Pythagorean theorem only for all right triangles.

Answer: B: False.

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