Question

Solve the triangle round to one decimal place

Answer 1

The missing angles are 74.6 degrees and 42.4 degrees while the missing side is 6.5 .

How to solve a triangle

To solve a triangle means to find the unknown sides and angles of a triangle, given some known information. The process varies depending on the given information and the type of triangle (e.g., right-angled, scalene, isosceles, or equilateral).

We know that;

`a^2` =
`b^2` +
`c^2` - 2abCosA

`a^2` =
`5^2`+
`7^2` - (2 * 5 *7) Cos 63

a = √
`5^2`+
`7^2` - (2 * 5 *7) Cos 63

a = √74 - 31.8

a = 6.5

Using the sine rule;

a/Sin A = b/Sin B

6.5/Sin 63 = 7/Sin B

Sin B = 7 * Sin 63/6.5

B = 74.6 degrees

Angle C = 180 - (74.6 + 63)

= 42.4 degrees