Question

Dr. Black is standing 13 feet from the streetlamp. The lamp is making his shadow 9 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the streetlamp is 50 degrees. To the nearest foot, the streetlamp is about _______

Answer 1

To the nearest foot, the streetlamp is about : 26 feet

Explanation:

We will use the trignometric ratio in the right angled triangle ΔABD in order to find the height of the streetlamp above the ground i.e. we need to find the value of x in ΔABD.

Hence, In ΔABD we have:

`\tan 50=(x)/(13+9)\\\\\\i.e.\\\\\\\tan 50=(x)/(22)\\\\i.e.\\\\x=22* \tan 50\\\\\\i.e.\\\\\\x=26.21857\ feet`

i.e. on rounding it to the nearest foot we get:

x=26 feet

Hence, the height of street lamp is:

26 feet

Answer 2

13 + 9 = 22 feet

the angle is 50 degrees

multiply 22 x tan(50) to find the height of the lamppost

22 x tan(50) = 26.21

so the lamppost is about 26 feet tall