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Lesson: Applications on Sine and Cosine Laws Mathematics

In this lesson, we will learn how to use the laws of sines and cosines to solve real-world problems.

Lesson Plan

Students will be able to

draw a diagram to represent a real-world problem and establish whether it can be solved by using the law of sines, the law of cosines, or a combination of both,
solve real-world problems using the law of sines, the law of cosines, or a combination of both, including finding unknown lengths and angle measures,
solve problems described using directions (north, east, south, and west) and problems given in a wider geometric context (including problems involving circles); this also includes finding areas of triangles or parallelograms.

Lesson Presentation

Lesson Video

Lesson Explainer

Lesson Playlist

03:30
03:49
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02:49

Lesson Worksheet

Q1:

A plane travels 800 meters along the runway before taking off at an angle of . It travels a further 1,000 meters at this angle as seen in the figure. Work out the distance of the plane from its starting point. Give your answer to 2 decimal places.

Q2:

is the center of a circle and , , and are points on the circumference. If and , find the area of the circle giving the answer to the nearest square centimeter.

Q3:

A biker traveled from city to city via city with a uniform speed of 52 km/h. He then returned directly to city with a uniform speed of 89 km/h. Find, in minutes, the total time of his whole journey to two decimal places.