Question

A plot of land is in the shape of a triangle. Two of the angles measure 48 degrees and 74 degrees. The length of the side between them is 90 m.

a) calculate the perimeter of the plot, to the nearest meter.

b) calculate the area of the plot, to the nearest square meter.

Answer 1

Perimeter = 271 meters

Explanation:

third angle measure would have to be 180 - 122 = 58 degrees

you can use the law of sines:

sin 58° = sin 74°

90 b

.85 = .96

90 b

cross-multiply: .85b = 86.4

b = 102

now do again to find third side:

sin 58° = sin 48°

90 c

.85 = .74

90 c

.85c = 67

c = 79

now you know all 3 sides so add them to get perimeter (79+102+90) = 271