A right triangle has hypotenuse 25cm and one leg 7cm. Its other leg is the adjacent side of a second right triangle at angle θ, where tanθ=21. Find the second triangle's opposite side x, in cm.
Linked right trianglesDiagram not to scaleShow worked answer
Answer: 12
First find the shared leg: √252−72=24cm.
Then opposite = adjacent ×tanθ
x=24×21=12cm.
Example 2
A right triangle has hypotenuse 60cm and an acute angle θ with sinθ=43. Its opposite leg is shared with a second right triangle whose hypotenuse is 51cm. Find the second triangle's other leg x, in cm.
Linked right trianglesDiagram not to scaleShow worked answer
Answer: 24
Shared leg=60×43=45cm.
Then x=√512−452=24cm.
Example 3
A right triangle has opposite leg 4cm at an acute angle θ with tanθ=21. Its adjacent leg is the length of a rectangle. The rectangle's width is 5cm greater than its length. Find the rectangle's area, in cm2.
Right triangleDiagram not to scaleShow worked answer
Answer: 104
tanθ=214=8cm.Rectanglelength=opposite
Width =8+5=13cm.
Area =8×13=104cm2.
Linked triangles and Pythagoras practice | Year 10 | Ascent Arcade