Question

1. find the height, x, of the tree. 40° 62 ft 52.02 ft 75.23 ft 73.89 ft 21.27 ft

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle with angle \(40^\circ\), adjacent side \(62\) ft, and opposite side \(x\) (height of tree). Use tangent: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\)
\(\tan(40^\circ)=\frac{x}{62}\)

Step2: Solve for \(x\)

Multiply both sides by \(62\): \(x = 62\times\tan(40^\circ)\)
Calculate \(\tan(40^\circ)\approx0.8391\), so \(x\approx62\times0.8391\approx52.02\)

Answer:

52.02 ft