Question

Find the area of triangle ABC as shown in the figure. Then find the distance across the pool (AB).

Answer 1

Given the figure, we can deduce the following information:

Angle C= 80°

AC=565 ft

BC=480 ft

To determine the area of the triangle ABC and the distance AB, we first

redraw the figure as shown below:

Next, we use the formula:

`c=√(a^2+b^2-2abcosC)`

where:

a=BC=480 ft

b=AC=565 ft

C= Angle C=80°

c=AB

We plug in what we know:

`\begin{gathered} c=√(a^2+b^2-2abcosC) \\ c=√(480^2+565^2-2(480)(565)cos80) \\ Calculate \\ c=AB=674.86\text{ }ft \end{gathered}`

Then, we get the area by using the formula:

`A=(absin\theta)/(2)`

where:

a=480

b=565

θ=80°

So,

`\begin{gathered} A=(abs\imaginaryI n\theta)/(2) \\ A=((480)(565)sin80)/(2) \\ Calculate \\ A=133539.93\text{ }ft^2 \end{gathered}`

Therefore, the answers are:

Distance AB=674.86 ft

Area of triangle ABC=133539.93 ft^2