Question

9. A building 62 feet tall casts a shadow 21 meters long. At what angle is the sun shining on the building?

A. 19.80
B. 18.71
C. 70.20
D. 71.29

Answer 1

71.29°

Explanation:

By question its given that , a 62 feet tall tree cast a shadow of 21 m long. We need to find the angle at which the sun is shining on the building .

For this we gonna imagine a right angle triangle . Where , the length of the shadow will be the base of the triangle and the height of the building will be the perpendicular on the triangle .

Here since we have got perpendicular and base , we can use the ratio of tan . We know that tan is defined as perpendicular by base , that is ,

`\implies tan \theta =(perpendicular)/(base)`

• where theta is the angle between the Ray of the the sun and the the shadow of the building.

Plug in the respective values , we have ,

`\implies tan \theta =(62)/(21) \\\\\implies\theta = tan^(-1)\bigg( (62)/(21)\bigg) \\\\\implies \underline{\underline{\theta = 71.29^o }}`

Hence the required answer is 71.29° .

Answer 2

First, we imagine a right triangle. Second, we are given that the building is 62 feet tall. Since the height of building is vertical straight - that means the height is opposite side of triangle. It also casts a shadow 21 meters long. Shadow should be the adjacent side because it casts on the ground and not on the air.

If we imagine the right triangle + the problem in our head, we'd get the triangle that the opposite side is 62 feet tall and the adjacent side is 21 meters long.

Use the tangent ratio to find the angle of sun shining.

`\large \boxed{ \tan \theta = (opposite)/(adjacent) }`

Substitute adjacent = 21 and opposite = 62 in the ratio.

`\large{tan \theta = (62)/(21) }`

For this part, you might need a calculator or trigonometric table because some values cannot be exactly found.

From the equation, we should get 71.288 which we round the answer to nearest hundreth and the answer would be 71.29

Answer

• The answer is 71.29