Question

Surveyors wished to know the distance across a lake between A and B. They measured the distance from B to C as 100 m and the angle from C to A to be 55°. Knowing that the angle between CB and BA was 90°, they used trig to solve for the distance. Show how it was done

Answer 1

Answer:

AB ≈ 70m

Step-by-step explanation:

Check the attachment for the diagram.

You can see from the diagram that it is a right angled triangle with opposite side AB and adjacent side BC. Using SOH, CAH, TOA trig identity to get the length of AB. According to TOA;

tan 35° = opposite/adjacent

tan 35° = AB/BC

tan 35° = AB/100

AB = 100tan35°

AB = 100 * 0.7002

AB = 70.02m

Hence the distance across a lake between A and B is approximately 70m