# Learning how to … use Pythagoras’ Theorem to calculate a shorter side of a right-angled triangle Mathematics GCSE Topic Reminders.

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Learning how to … use Pythagoras’ Theorem to calculate a shorter side of a right-angled triangle Mathematics GCSE Topic Reminders

We already know how to … identify the hypotenuse … Hypotenuse Opposite the right angle

We already know … Pythagoras ’ Theorem … += For a right-angled triangle … Hypotenuse Biggest square …on its own

We already know … Pythagoras ’ Theorem … += For a right-angled triangle … Biggest square a b c a2a2 b2b2 c2c2 a2a2 b2b2 c2c2

3, 4, 5 example 16 + 9 = 25

We already know … Pythagoras ’ Theorem … += Biggest square a b c We don’t need to keep drawing the squares … a2a2 b2b2 c2c2 a2a2 b2b2 c2c2

We already know how to … square a number … 7272 means … 7 x 7= 49 4.8 2 on a calculator … 4.8 x 4.8 or … NOT 7 x 2

23.04

We already know how to … find the square root of a number …  36 means … ? x itself = 36 i.e. 6  52 on a calculator … because 6 x 6 = 36

23.04 7.2 to 1dp 7.21110255

We already know how to … calculate the hypotenuse … += Biggest square 4.7 6.2 c 4.7 2 6.2 2 c2c2 4.7 2 6.2 2 c2c2 + =22.0938.44c2c2 =60.53c2c2 =  60.53c =7.8c

We will now learn how to … calculate a shorter side … Shorter side Hypotenuse

Identify the hypotenuse … opposite the right angle Label the unknown side x

Write down the square of each side Write Pythagoras’ Rule using these squares x x2x2 16.5 2 12.8 2 Biggest square x2x2 + 12.8 2 = 16.5 2 GCSE 1 st

Rearrange to leave x 2 on its own x x2x2 +12.8 2 =16.5 2 x 2 = 16.5 2 - 12.8 2 x2x2 -163.84=272.25 Calculate the right hand side to give x 2 x 2 = 108.41 GCSE 2 nd

Find the  of this to give x x 2 = 108.41 x =  108.41 Write answer to appropriate degree of accuracy and refer to original question x = 10.41201 radius = 10.4 cm x GCSE 3 rd

Calculate the length of AC, giving your answer to a suitable degree of accuracy. Calculate the length of AD, giving your answer to a suitable degree of accuracy.

PQRS is a parallelogram with SR = PQ = 15.6 and PS = QR = 9.8cm. M is the foot of the perpendicular from P onto SR and SM = 4.7cm. Find the length of PM.

Use Pythagoras’ Theorem to calculate the height marked h.

Learning how to … use trigonometry to find an angle in a right angled triangle. Mathematics GCSE Topic Reminders

We already know how to … label the sides … x Opposite Hypotenuse Opposite the right angle Adjacent Opposite the angle we need Next to the angle we need

We already know … The formula for SINE … x Opposite Hypotenuse Sin x = Opposite Hypotenuse Adjacent

We already know … The formula for COSINE … x Opposite Hypotenuse Cos x = Adjacent Hypotenuse Adjacent

We already know … The formula for TANGENT … x Opposite Hypotenuse Tan x = Opposite Adjacent

Don’t use a protractor

Label the given sides in relation to the angle you need to find Opposite Hypotenuse Adjacent

Opposite Choose SIN, COS or TAN depending on the sides given ‘Opposite’ & ‘Adjacent’ means we’ll be using TAN for this question Adjacent

Opposite Adjacent Write out the formula with correct numbers Tan x = 138opposite 177adjacent GCSE 1 st

Opposite Adjacent Tan x = 138 177 Key 2 nd (or INV ) TAN 138  177 = into the calculator to give the angle x Calculator set to DEG x = 37.9 o GCSE 2 nd & 3 rd

Calculate the size of BĎE.

Calculate the length of BE.

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