Question

SA A4 At tall child creates a shadow that is 7.5 ft long. What is the angle of elevation of the sun? 28 degrees 62 degrees 49 degrees 15 degrees

Answer 1

hello

to solve this question, we would first of all sketch the probelm to give us a better understanding of what we need to do

from the figure above, we can proceed and use trigonometric ratio to find the missing angle

`\begin{gathered} \text{SOHCAHTOA} \\ \text{SOH}=\sin \theta=(opposite)/(hypothenus) \\ \text{CAH}=\cos \theta=(adjacent)/(hypothenus) \\ \text{TOA}=\tan \theta=(opposite)/(adjacent) \end{gathered}`

from the question, we have the values of adjacent and hypothenus and we can simply apply tangent to find the angle.

`\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ opposite=4 \\ adjacent=7.5 \\ \tan \theta=(4)/(7.5) \\ \tan \theta=0.53 \\ \text{take the tangent inverse of 0.53} \\ \theta=\tan ^(-1)0.53 \\ \theta=27.92\approx28^0 \end{gathered}`