Question

The area of the triangle below is 17.8cm^2.

work out the size of angle ∅, given that it is acute.
give your answer in degrees (°) to s.f.

Answer 1

Set your calculator to Degree mode.

(1/2)(11.3)(5.2)(sin A) = 17.8

29.38sinA = 17.8

sin A = 890/1,469

A = sin^-1 (890/1,469) = 37.3°

Answer 2

The size of angle θ is 39.3°.

To find the size of angle θ, we can use the sine rule:

sin(A)/a = sin(B)/b = sin(C)/c

where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the corresponding sides.

We know that the area of the triangle is 17.8 cm², so we can use the formula for the area of a triangle to find the length of side c:

Area = 1/2 * base * height

17.8 = 1/2 * 5.2 * c

c = 6.8 cm

Now that we know the lengths of all three sides of the triangle, we can use the sine rule to find the size of angle θ:

sin(51°)/6.8 = sin(\theta)/5.2

sin(\theta) = sin(51°) * 5.2 / 6.8

sin(\theta) = 0.64

\theta = asin(0.64)

\theta = 39.3°

Therefore, the size of angle θ is 39.3°.