Question

1. find the length of each side labelled with a variable. (answers to 1 decimal place)

a)
8 cm
6 cm

h
e)
12 cm
15 cm

Explanation:

Step1: Apply Pythagorean theorem for part a

For a right - angled triangle with sides \(a = 6\mathrm{cm}\), \(b = 8\mathrm{cm}\) and hypotenuse \(h\), by the Pythagorean theorem \(h=\sqrt{a^{2}+b^{2}}\).
\[h=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10\mathrm{cm}\]

Step2: Apply Pythagorean theorem for part e

Let the unknown side be \(x\). Given one side \(a = 12\mathrm{cm}\) and hypotenuse \(c = 15\mathrm{cm}\). By the Pythagorean theorem \(x=\sqrt{c^{2}-a^{2}}\).
\[x=\sqrt{15^{2}-12^{2}}=\sqrt{(15 + 12)(15 - 12)}=\sqrt{27\times3}=\sqrt{81}=9\mathrm{cm}\]

Answer:

a) \(h = 10.0\mathrm{cm}\)
e) The unknown side is \(9.0\mathrm{cm}\)