Question

In a certain triangle two sides have lengths 5 and 13. The angle between them is 49

degrees. What is the area of the triangle?

Answer 1

Area = 24.54

Explanation:

two sides have lengths 5 and 13.

Let the two sides be;

a = 5

b = 13

The angle between them is 49

C = 49°

Let the third side be c

Thus, using cosine rule, we can find the side c.

c² = a² + b² - 2ac•Cos C

Plugging in the relevant values, we have;

c² = 5² + 13² - 2(5 × 13)Cos 49

c² = 25 + 169 - 130(0.6561)

c² = 108.707

c = √108.707

c = 10.43

Since we now have 3 sides, from herons formula, we can find the area;

Area = √[p(p − a)(p − b)(p − c)]

Where p is half of the perimeter = (a + b + c)/2 = (5 + 13 + 10.43)/2 = 14.215

Thus;

Area = √(14.215(14.215 - 5)(14.215 - 13)(14.215 - 10.43))

Area = √602.4

Area ≈ 24.54