A right triangle has one angle that measure 23. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle?

Given for the Right Triangle:

∠A = 23°

a (height) = 27.6cm

c (hypotenuse) = 30cm

Find:

b (base) = ?

Area of the Triangle = ?

Solution:

The formula for the area of triangle is: [ b*h]:2; where b is base and h is height

Since you do not have the sides for the base, let's find it first before we can find the area.

To find the b (base), we will use the law of cosine. Specifically the cos∠ = adjacent side:hypotenuse

The ∠ that you should use is the angle that is adjacent to b (base) which is the ∠A

That makes the law of cosine formula into: cos∠A = b:c

Let's derive the formula to the side that we are looking for:

Find a (height)

b = cos∠A*c

b = cos23 °*30cm; substituting the numbers

b = 27.6151cm

Now that there is a base, you can now find the area of the triangle.

Area of Triangle = [b * h]:2

Area of Triangle = [27.6151cm * 27.6cm]:2

Area of Triangle = 381.0883cm ²; Final Answer