Question

the house from the base of the cliff?
\\(\tan38^{circ}20=\frac{500}{x})\\
\\(0.7907 = \frac{500}{x})\\
\\(0.7907x = 500)\\
\\(x = 632.4)\\
\\(632m)

Explanation:

Step1: Recall tangent formula

The tangent of an angle in a right - triangle is $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 38^{\circ}20'$, the opposite side is 500 and the adjacent side is $x$. So, $\tan38^{\circ}20'=\frac{500}{x}$.

Step2: Substitute the value of tangent

We know that $\tan38^{\circ}20'\approx0.7907$, so $0.7907=\frac{500}{x}$.

Step3: Cross - multiply

Cross - multiplying gives $0.7907x = 500$.

Step4: Solve for $x$

Dividing both sides by 0.7907, we get $x=\frac{500}{0.7907}\approx632.4$. Rounding to the nearest whole number, $x = 632$ m.

Answer:

632 m