Question

Find the value of z.

15 cm
5 cm
82=
20 cm
Give your answer correct to 1
decimal place.
Z
Submit Answer
cm

Answer 1

z=12.25

Explanation:

first we are going to find the hypotenus x

of the first part of the tiangle as shown in my diagram, using the Pythagoras rule-

hyp= x

opp= 15

adj=5

thus hypothenus²=opposite²+adjacent²

x²=15²+5²

x²=225+25

x²=250

the you use √ to find x

√x²=√250

x=15.81

step 2= to find z

hyp=20

opp:z

adj:15.81

hyp²=opp²+adj²

20²=z²+15.81²

400=z²+250

z²+250=400

z²=400-250

z²=150

√z²=√150

z=12.25

Answer 2

z ≈ 12.2 cm

Explanation:

using Pythagoras' identity in the 2 right triangles.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

consider the right triangle on the left

let the third side, the hypotenuse be x , then

x² = 5² + 15² = 25 + 225 = 250

consider the right triangle on the right , then

x² + z² = 20²

250 + z² = 400 ( subtract 250 from both sides )

z² = 150 ( take square root of both sides )

z =
`√(150)` ≈ 12.2 cm ( to 1 decimal place )