Question

To the nearest whole number what is the distance across the lake?

Answer 1

x=296 yd

STEP - BY - STEP EXPLANATION

What to find?

The value of x.

Given:

From the above figure;

side a=x

angle A = 70 degree.

side b = 245 yd

side c = 270 yd

Since , we have just one angle, we will use the cosine formula below:

$a^2=b^2+c^2-2bc\cos A$

Substitute the values into the formula.

$x^2=245^2+270^2-2(245)(270)\cos 70\degree$$x^2=60025+72900-132300\cos 70\degree$$x^2=132925-45249.264962$$x^2=87675.735038$

Take the square root of both-side of the equation.

$x\approx296$

Therefore, the distance across the lake is 296yd.