Question

Use trigonometry to find the height of the triangle. Then use the height to find the area. Round to the nearest hundredth

Answer 1

Answers:

height = 4.46 units

area = 26.73 square units

Both values are approximate

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Explanation:

h = height of the triangle

Focus on the smaller triangle on the left.

Use the cosine ratio to find h

cos(angle) = adjacent/hypotenuse

cos(27) = h/5

h = 5*cos(27)

h = 4.4550326 approximately

Your calculator needs to be in degree mode.

We can now find the area of the overall largest triangle.

area = 0.5*base*height

area = 0.5*12*4.4550326

area = 26.7301956

area = 26.73

Answer 2

Answer with a step-by-step explanation:

1) First, let us find the height of the triangle.

For that let us use cos theta to find the triangle's height.

Let us use the below formula to find it.

cos Θ = Adjacent ÷ hypotenuse

Let the height (adjacent ) be h.

Let us find it now.

cos Θ = Adjacent ÷ hypotenuse

cos 27° = h ÷ 5

0.8910 = h ÷ 5

0.8910 × 5 = h

4.455 = h

Therefore the height of the triangle is 4.455 units.

                                                                                                       

2) And now let us find the area of the triangle.

The formula to find the area of a triangle is:

Area =  $\frac{1}{2}$ × base × height

Let us find it now.

A =  $\frac{1}{2}$ × base × height

A =  $\frac{1}{2}$ × 12 × 4.455

A =  $\frac{1}{2}$ × 53.46

A = 26.73 units²