Question

Solve each triangle for the missing values shown. Show all work necessary. Use exact values

Answer 1

3)

$Cos 60°= \frac{1}{2} = \frac{Adjacent} {Hypotenuse} = \frac{y} {10} \\\\ 2y=10 \\\\ y=5$

Now, use Pythagoras theorem to find x

$x^2+y^2=10^2 \\\\ \to x^2+5^2=10^2 \\\\ \to x^2+25=100 \\\\ \to x^2 = 100-25 \\\\ \to x^2= 75 \\\\ \to x= \sqrt{75} \\\\ \bf 5 \sqrt{3}$

Similarly,

4)

$Sin 45°= \frac{1}{\sqrt{2}} = \frac{Opposite} {Hypotenuse} =\frac{2 \sqrt{2}} {a} \\\\ a= 2 \sqrt{2} \times \sqrt{2} \\\\ a=4$

Now, use Pythagoras theorem to find b

$b^2+(2 \sqrt{2}) ^2=a^2 \\\\ \to b^2+8=4^2 \\\\ \to b^2=16-8 \\\\ \to b^2 = 8\\\\ \to b= \sqrt{8} \\\\ \bf b=2 \sqrt{2}$

You can solve all of them in a similar way.

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