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In this lesson, we will learn how to use the properties of a 45-45-90 triangle to find the lengths of the legs or the hypotenuse.

Q1:

A ladder 8 metres long leans against a wall. Find the horizontal length between the base of the ladder and the wall given the angle between the ladder and the ground is 4 5 ∘ .

Q2:

Find, in terms of 𝑥 , the length of the hypotenuse of this triangle.

Q3:

In the figure, the length of 𝐴 𝐵 is √ 8 .

Find the length of 𝐵 𝐶 .

Given that the length of 𝐷 𝐸 is 6, find the length of 𝐶 𝐸 . Give an exact answer.

Q4:

Use the figure to find the value of .

Q5:

Given that 𝐴 𝐵 = 3 , find 𝐵 𝐶 . Give an exact answer.

Q6:

Find the ratio of the length of 𝐴 𝐵 to the length of 𝐵 𝐶 in its simplest form.

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