Unit 8 right triangles and trigonometry homework 2 answers key


Asked by maham237 @ in Mathematics viewed by 508 People


Answered by maham237 @



Answer:

Part 1) x=14\sqrt{2}\ units

Part 2) y=14\ units

Part 3) z=14\sqrt{3}\ units

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ABC

we know that

The triangle ABC is a 45^o-90^o-45^o

so

Is an isosceles right triangle

The legs are equal

therefore

AC=AB

x=14\sqrt{2}\ units

step 2

Find the length side BC

Applying the Pythagorean Theorem]

BC^2=AB^2+AC^2

BC^2=(14\sqrt{2})^2+(14\sqrt{2})^2

BC^2=784\\BC=28\ units

step 3

Find the value of y

In the right triangle BCD

sin(30^o)=\frac{BD}{BC} ----> by SOH (opposite side divided by the hypotenuse)

sin(30^o)=\frac{y}{28}

Remember that

sin(30^o)=\frac{1}{2}

so

\frac{y}{28}=\frac{1}{2}\\\\y=14\ units

step 4

Find the value of z

In the right triangle BCD

cos(30^o)=\frac{DC}{BC} ----> by CAH (adjacent side divided by the hypotenuse)

cos(30^o)=\frac{z}{28}

Remember that

cos(30^o)=\frac{\sqrt{3}}{2}

so

\frac{z}{28}=\frac{\sqrt{3}}{2}\\z=14\sqrt{3}\ units


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