If b is the base, identify the perpendicular height of this triangle.

Find the perpendicular height of the triangle.

Find the perpendicular height of the triangle. Give your answer to one decimal place.

Use trigonometry to find the perpendicular height of a triangle

﻿Oh, hi. I'm Mrs. Dennett. And in this lesson, we're going to be solving basic trigonometry equations. So, you're going to be needing one of these. Now, don't worry if you haven't got access to a scientific calculator. There are lots of free online ones. Just ask your parent or carer to search for one online and you'll be ready for this lesson. Have you got your calculator ready? Excellent. So firstly, make sure that your calculator is working in degrees mode. You can usually tell that your calculator is in degrees mode by looking for a D at the top of the calculator display. If not, you'll need to look up how to change this before you start. We're asked to work out the value of sine, or sin as we abbreviate it to, sin32. So, the angle is 32 degrees, and we want to work out the sine of the angle 32. So, we use these buttons on our calculator. Now, many calculators come with a bracket at this point when you've typed in sin. But if yours doesn't, don't worry. You'll just have to remember to type it in. Then press three and two, and you can close the brackets at this point because we've typed in our angle, though not all calculators require this step, and then press equals. And the answer should appear on your calculator display. We want to carefully round this to three decimal places. So, we get sin32 equals 0.530. Let's try another trigonometry equation. So, we have tan29. So, make sure your calculator is in degrees mode first and then type tan followed by the equal sign, and we get this answer here. So, to three decimal places, we get 0.554. In this next example, we want to find the value of the angle theta to the nearest degree. When sine theta equals 0.6 or sin theta equals 0.6 depending on how you want to say it. So, for this example, we have to use inverse sine or sin to the minus one. And we find this on most calculators by pressing the shift button and then the sin button. And you'll see that this gets us sin to the minus one on our display. This sin to the minus one is written just above the symbol on your calculator. So, that's how we find it. We have to press Shift first and then we have to type in 0.6, close the bracket, if you need to, but most calculators at this point just allow you to press equals. And you can check that you've got this answer, 36.86989765, which means that to the nearest degree or the nearest whole number, theta is 37 degrees. Let's try using the inverse of cosine this time to find the angle of theta. So, make sure your calculator is in degrees mode, then type in Shift and cos to get cos to the minus one. Some of you have all made the first bracket at this point, that's fine, putting 0.8 and press equals. And we get 36.86989765, which, amazingly, is the same decimal as last time, inverse sin of 0.6. So, if you want to learn more about why you get the same answer for these two particular trigonometric ratios, trigonometric equations, then just watch the advanced trigonometry three lessons. And then all I have to do now is round this answer to the nearest degree, which is 37 degrees. So, theta equals 37 degrees. Here is a question for you to try. Pause the video to complete the task and restart when you are finished. Here are the answers. Nothing too difficult in this first set of questions, I hope, as long as your calculator was in degrees mode. For question two, however, you'll notice that we've used function machines. Well, it would be rude not to given that we are working with sine, cos, and tan functions, but we'll just be careful. It does tell you which buttons to press, but you have to remember that for the inverse functions, you have to use the shift button. So, Shift+sin and Shift+tan, and then you'll find the missing angles. Here are some more questions for you to try. Pause the video to complete the task and restart when you are finished. Here are the answers. All the questions required the inverse function, and we've even got a couple of fractions thrown in to keep us on our toes. You may have used the fraction button for this or the fact that five eighteenths is also a five divided by 18. So, just put five divided by 18 in the bracket after the function and press the equal sign. That's all for this lesson. Remember to take the exit quiz before you leave. Thank you for watching.

Use your calculator find the value of cos(56) to 3 decimal places.

Use your calculator find the value of tan(89) to 3 decimal places.

3. Use your calculator to work out the size of sinѲ = 0.21 . Give your answer to one decimal place.

Solve basic Trigonometry equations

In this lesson, we will use a calculator to work out values of angles by rearranging trigonometric equations relating to sides and angles and using inverse trigonometric functions.

Maths

Y10 Maths (Higher)

Key Stage 4

Year 10

Solve basic trigonometry equations

Y10 Maths (Core)

Trigonometry 2

Shape and Space (S)

THEME

UNIT

Use inverse functions to find an angle

Solve problems mixing angles and sides

Which of the trigonometry ratios will be required to find the missing angle in this question?

Find the missing angle, giving your answer to 1 decimal place.

To find x, which other side will you need to find first

2.Work out the length of the side marked x to 2 d.p.

A ladder that is 5 metres long is placed against a wall. The angle of elevation is 50°. How high up the wall does the ladder reach? Give your answer to 2 d.p.

Lesson overview:Solve basic trigonometry equations

Core Content

Trigonometry 2: