3.03 Finding a short side

Find the number that completes a Pythagorean triple given the following:

For the following right-angled triangles:

a

b

c

Find the length of the unknown side of the following triangles:

a

b

c

d

e

f

Find the length of the unknown side of the following triangles, correct to two decimal places:

a

b

c

d

e

f

g

h

Find the length of the unknown side of the following triangles, giving your answer as a surd:

a

b

The two short sides of a triangle have lengths of 10 and 17. Sarah notices that she can divide the triangle into two smaller right-angled triangles, each with a height of 8.

a

Find the base lengths of the two right-angled triangles.

b

Find the base length of the original triangle.

Find the base length of the following triangles:

a

b

Consider a right-angled triangle with hypotenuse of length 15 \,\text{cm} and another side of length 4 \,\text{cm}.

Consider a rectangle with a diagonal of length 25 \,\text{cm} and a side of length 24 \,\text{cm}.