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Pls help solve for A

A= Pls help solve for A-example-1

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1 vote

Answer:

a=3.75 un., b=11.25 un.


x=7.5\ un.


y=(15√(3))/(4)\ un.


z=(15√(3))/(2)\ un.

Explanation:

Given triangle is special 30°-60°-90° right triangle. The leg that is opposite to the angle of measure 30° is always equal to half of the hypotenuse. The hypotenuse is of length 15 units, the leg that is opposite to the 30° angle is leg with length of x units, then


x=(15)/(2)=7.5\ un.

In right triangle with hypotenuse x and legs y and a, angle opposite to the leg a is 30°, then


a=(x)/(2)=(7.5)/(2)=3.75\ un.

and


b=15-a=15-3.75=11.25\ un.

By the Pythagorean theorem,


x^2=y^2+a^2,\\ \\7.5^2=3.75^2+y^2,\\ \\y^2=\left((15)/(2)\right)^2-\left((15)/(4)\right)^2=(225)/(4)-(225)/(16)=(675)/(16),\\ \\y=(15√(3))/(4)\ un.

In right triangle with legs y and b and hypotenuse z, leg y is opposite to 30° angle, then


z=2y=(15√(3))/(2)\ un.


User Macwadu
by
8.0k points
5 votes

Answer:


a=3.75


Explanation:

The hypotenuse of the large triangle is 15.

We can see that the side opposite of 30° angle is
x

Trigonometric ratio of SINE relates opposite and hypotenuse.


Thus we can write and cross multiply and solve:


sin(A)=(Opposite)/(Hypotenuse)\\sin(30)=(x)/(15)\\x=15*sin(30)=7.5


Now if you see the smallest triangle,
a is the adjacent side
and
x becomes the hypotenuse
of this triangle.

Trigonometric ratio of COSINE relates adjacent and hypotenuse.


Thus we can write and cross multiply and solve:


cos(A)=(Adjacent)/(Hypotenuse)\\cos(60)=(a)/(7.5)\\a=7.5*cos(60)=3.75

Thus
a=3.75


User Divyanth Jayaraj
by
8.5k points

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