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 [tex]m\angle P = 78^{\circ}[/tex]
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,
[tex]\text {Area}=\frac{1}{2} qr \sin P[/tex]
Substituting the values, we get,
[tex]\text {Area}=\frac{1}{2}(12)(3) \sin 78[/tex]
Simplifying, we have,
[tex]\text {Area}=\frac{1}{2}(36)(0.98)[/tex]
Multiplying the terms, we have,
[tex]\text {Area}=\frac{35.28}{2}[/tex]
Dividing, we get,
[tex]\text {Area}=17.64[/tex]
Rounding off to the nearest tenth, we have,
[tex]Area=17.6[/tex]
Thus, the area of the triangle PQR is 17.6 square units.
Answer:
17.6 units²
Step-by-step explanation:
Area = ½ × PQ × PR × sin(P)
= ½ × 12 × 3 × sin(78)
= 17.6066568132
