Question

Trigonometry

Answer 1

Answer:

17.6 units²

Step-by-step explanation:

Area = ½ × PQ × PR × sin(P)

= ½ × 12 × 3 × sin(78)

= 17.6066568132

Answer 2

The area of the triangle PQR is 17.6 square units.

Explanation:

Given that the sides of the triangle are PQ = 12 and PR = 3 and $m\angle P = 78^{\circ}$

We need to determine the area of the triangle PQR

Area of the triangle:

The area of the triangle can be determined using the formula,

$\text {Area}=\frac{1}{2} qr \sin P$

Substituting the values, we get,

$\text {Area}=\frac{1}{2}(12)(3) \sin 78$

Simplifying, we have,

$\text {Area}=\frac{1}{2}(36)(0.98)$

Multiplying the terms, we have,

$\text {Area}=\frac{35.28}{2}$

Dividing, we get,

$\text {Area}=17.64$

Rounding off to the nearest tenth, we have,

$Area=17.6$

Thus, the area of the triangle PQR is 17.6 square units.