Question

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

Answer 1

3)

`Cos 60°= (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= √(75) \\\\ \bf 5 √(3)`

Similarly,

4)

`Sin 45°= (1)/(√(2)) = \frac{Opposite} {Hypotenuse} =\frac{2 √(2)} {a} \\\\ a= 2 √(2) * √(2) \\\\ a=4`

Now, use Pythagoras theorem to find b

`b^2+(2 √(2)) ^2=a^2 \\\\ \to b^2+8=4^2 \\\\ \to b^2=16-8 \\\\ \to b^2 = 8\\\\ \to b= √(8) \\\\ \bf b=2 √(2)`

You can solve all of them in a similar way.

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