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The Laws of Sines and Cosines · Paper 2 — Free Maths AI SL Practice Questions

1MasterySAQ-SLaw of Sines and its applications6 marksPaper 2~9 min

Data

a^2 = b^2 + c^2 - 2bc\cos A \qquad \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

A surveyor needs to determine the distance across a river. She marks point

A

one bank, and points

B

and

C

on the opposite bank, where

A

B

C

form a triangle. She measures

AB = 85.0\,\text{m}

AC = 112.0\,\text{m}

, and the angle

B\hat{A}C = 47.0°

(a)

Calculate the length

BC

. [3 marks]

(b)

The surveyor places a marker at point

D

on the same bank as

A

, such that

A

C

, and

D

are collinear (i.e.

D

lies on the line

AC

extended beyond

C

). Triangle

BCD

isosceles with

BC = CD

. Calculate the angle

B\hat{D}C

. [3 marks]

Solutions

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