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Aneli [31]
3 years ago
11

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

Mathematics
1 answer:
Gelneren [198K]3 years ago
7 0

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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