Using inverse sine and cosine to find missing angles
Using inverse sine and cosine to find missing angles
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Lesson details
Key learning points
- In this lesson, we will use inverse sine and cosine to find missing angles in triangles.
Licence
This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.
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7 Questions
Q1.
What is the length of side marked q ?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707169159%2Fbasabq2jhm18wky5sona.png&w=384&q=75)
10 cm
5 cm
Q2.
What is the length of the side marked r ?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707169161%2Fvkfe4hsj3nl6bkamu2jp.png&w=828&q=75)
15 cm
22 cm
Q3.
What is the correct step for calculating the length of side b?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707212430%2Fe9nhh5se8voysfzlsmx7.png&w=640&q=75)
![](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707137962%2Fxctmgnoknq9piej1aow1.png&w=640&q=75)
![](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707199172%2Fnbti45qkso715dqgniv2.png&w=640&q=75)
Option 2
![](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707201955%2Fd644hjmbebcjruj1rb6l.png&w=640&q=75)
Option 3
Q4.
What is the length of of b correct to 1 decimal place?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707169188%2Feycpd22h2djqokk7ic41.png&w=640&q=75)
0.86 cm
10 cm
Q5.
What is the correct step for calculating the length of side a?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707169202%2Fzmlmrwg93aimwmrb8h4o.png&w=640&q=75)
![](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707137973%2Fwfh0z9ya2ukac5uua304.png&w=640&q=75)
Option 1
![](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707139311%2Fzjyidfhnpw7xx1f3r0uz.png&w=640&q=75)
Option 2
![](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707140352%2Fbvx3ogrp6glsrmskivt9.png&w=640&q=75)
Q6.
What is the length of a, correct to 1 decimal place?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707169216%2Fjpyazk8c3guyrxtyztjl.png&w=640&q=75)
0.5 cm
23 cm
39.2 cm
Q7.
Which ratio would you use to find the length of the missing side in the triangle below?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707169224%2Foi6dtvs8rqfvbvoruyx9.png&w=384&q=75)
pythagoras
sine
6 Questions
Q1.
Fill in the gap: You can use the inverse sine function to work out the unknown angle, when given the opposite and ................. in a right- angled triangle.
adjacent
symmetry
Q2.
Fill in the gap: You can use the inverse cosine function to work out the unknown angle, when given the hypotenuse and ................. in a right- angled triangle.
opposite
symmetry
Q3.
Use the sine ratio to find out the missing angle in the triangle shown below.
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707169854%2Fwefvxpxwiknijsctubtb.png&w=384&q=75)
15 degrees
45 degrees
60 degrees
Q4.
Which is the correct method to work out the missing angle?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707169861%2Fo5zx5ijetzmew95doqoy.png&w=384&q=75)
Pythagoras
Sine
Q5.
Which is the correct method to work out the missing angle?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707169868%2Fibcdkygfplgwrmqnweb5.png&w=640&q=75)
Cosine
Pythagoras
Q6.
Which is the correct method to work out the length of missing side?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707169881%2Fgbegusjyp4neqksv8bsg.png&w=750&q=75)
Pythagoras
Sine