Question

Find the area of the triangle below.Carry your intermediate computations to at least four decimal places. Round your answer to the nearest hundredth.348 in13 in

Answer 1

Answer:

Explanation:

Let us call h the height of the triangle and b its base length.

Then the area of the triangle is

$A=\frac{1}{2}h\cdot b$

Now in our case, the height h is given by

$\sin 34=\frac{h}{8}$

Multiplying both sides by 8 gives

$h=8\sin 34$

therefore, the area is

$A=\frac{1}{2}(8\sin 34)\cdot b$

since b = 13 in, the above becomes

$A=\frac{1}{2}(8\sin 34)\cdot13$

which simplifies to give

$A=8\cdot\frac{1}{2}\cdot13\cdot\sin 34$$A=52\sin 34$

Since sin 34 = 0.5591, the above becomes (rounded to the nearest hundredth)

$A=29.08$

which is our answer!

Hence, the area of the triangle is 29.08 square inches.