This question explores trigonometry applications All calcula

This question explores trigonometry applications. All calculations must be shown in detail, Draw triangle sketches clearly Suppose a landscaper is asked by a client a triangular garden space where angle A is 37 degrees, side a is 30 ft and side c is 40 feet, check it out and see if this is possible, if so, state what you would tell the surveyor to do.

Solution

side a = 30ft angle A opposite to this side = 37 deg

side c = 40 ft

Apply sine rule: a/sinA = c/sinC

sinC = c*sinA/a = 40*sin37/30 = 0.8

angle C = 53.36 deg

So, this triangle is possible as sinC <|1|

We can gve the surveyor all the remaining information regarding the triangle:

C = 53.36 deg ; angle B = 180 -A - C = 89.64 deg

lenght of side b : b/sinB = a/sinA

b = sin89.64*30/sin37 = 49.85 feet