Can someone help me with these and please show work and explain because I don’t really get it :(

Mathematics

1 answer:

stich3 [128]3 years ago

7 0

The acronym: SOH CAH TOA
Stands for;
Sin(x) = Opposite / Hypotenuse
Cos(x) = Adjacent / Hypotenuse
Tan(x) = Opposite / Adjacent

What you have written on the triangle. The angle is what goes inside the trig functions (Sine, Cosine, Tangent). The side opposite of the 36° angle is MP. The Hypotenuse of the triangle (always the longest side) is side PN. The Adjacent side to the 36° angle is given to be 28.

Use trig functions containing the given Adjacent side to solve for the missing sides Opposite, P and Hypotenuse, H .

Opposite side (calling it "P")
Tan(36°) = P / 28
multiply by 28 on both sides
28 × Tan(36°) = P
20.34 = P

Hypotenuse of the triangle (H)
Cos(36°) = 28 / H
Cross multiply
H = 28 / Cos(36°)
H = 34.61

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<u>SOLUTION: </u>

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$\begin{array}{l}{\text { Distance between }(-5,-1) \text { and }(-5,5)=\sqrt{(-5-(-5))^{2}+(5-(-1))^{2}}} \\\\ {\qquad \begin{array}{l}{=\sqrt{(-5-(-5))^{2}+(5-(-1))^{2}}} \\\\ {=\sqrt{(0)^{2}+(5+1)^{2}}=\sqrt{(6)^{2}}=6} \\\\ {=\sqrt{(-5)^{2}+(5+1)^{2}+(5-(-1))^{2}}} \\\\ {=\sqrt{(-8)^{2}+(5+1)^{2}}=\sqrt{64+36}=\sqrt{100}=10} \\\\ {=\sqrt{(3-1)^{2}+(-1-(-1))^{2}}} \\\\ {=\sqrt{(5+3)^{2}+(0)^{2}}=\sqrt{(8)^{2}}=8}\end{array}}\end{array}$