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

Explanation:

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

Then the area of the triangle is

`A=(1)/(2)h\cdot b`

Now in our case, the height h is given by

`\sin 34=(h)/(8)`

Multiplying both sides by 8 gives

`h=8\sin 34`

therefore, the area is

`A=(1)/(2)(8\sin 34)\cdot b`

since b = 13 in, the above becomes

`A=(1)/(2)(8\sin 34)\cdot13`

which simplifies to give

`A=8\cdot(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.