Question

Dr. Black is standing 15 feet from a streetlamp. The lamp is making his shadow 8 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the street lamp is 50. To the nearest foot, the streetlamp is about _____.

Plz help.

Answer 1

Height of the street lamp = 27.42 feet

Explanation:

Distance of Mr. Black from streetlamp = 15 feet

Length of shadow = 8 feet

Total distance from tip of the building to the shadow = 15 + 8

= 23 feet

Angle of elevation = 50°

Let height of street lamp be x feet

Now, the height of the street lamp is perpendicular to the ground surface. So a right angled triangle is formed

Hence by using property of tan in the triangle formed :

`\tan 50=\frac{\text{height of street lamp}}{\text{Total distance from tip of the building to shadow}}\\\\\tan 50=(x)/(23)\\\\\implies x=1.192* 23=27.42\\\\\bf\implies\textbf{Height of the street lamp = }27.42\thinspace{ feet}`

Answer 2

ythe base of the triangle is 15 + 8 = 23 feet

and the angle is 50 degrees

to find the height of the street lamp

multiply the base ( 23) by the Tan(50)

tan(50) x 23 = 27.41 feet rounded to nearest foot would be 27 feet