Question

how tall is the tree? 75 ft, 40°, h, 63 ft, 18 ft, 44 ft, 27 ft

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle with an angle of \(40^\circ\), the adjacent side to the angle is \(75\) ft, and we need to find the opposite side (height of the tree, \(h\)). We use the tangent function, which is \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\).
So, \(\tan(40^\circ)=\frac{h}{75}\)

Step2: Solve for \(h\)

We know that \(\tan(40^\circ)\approx0.8391\) (using a calculator). Then we can solve for \(h\) by multiplying both sides of the equation by \(75\):
\(h = 75\times\tan(40^\circ)\)
\(h\approx75\times0.8391\)
\(h\approx62.9325\approx63\) ft

Answer:

63 ft