Question

A=
Pls help solve for A

Answer 1

Answer:

a=3.75 un., b=11.25 un.

$x=7.5\ un.$

$y=\dfrac{15\sqrt{3}}{4}\ un.$

$z=\dfrac{15\sqrt{3}}{2}\ un.$

Step-by-step 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

$x=\dfrac{15}{2}=7.5\ un.$

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

$a=\dfrac{x}{2}=\dfrac{7.5}{2}=3.75\ un.$

and

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

By the Pythagorean theorem,

$x^2=y^2+a^2,\\ \\7.5^2=3.75^2+y^2,\\ \\y^2=\left(\dfrac{15}{2}\right)^2-\left(\dfrac{15}{4}\right)^2=\dfrac{225}{4}-\dfrac{225}{16}=\dfrac{675}{16},\\ \\y=\dfrac{15\sqrt{3}}{4}\ un.$

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

$z=2y=\dfrac{15\sqrt{3}}{2}\ un.$

Answer 2

Answer:

$a=3.75$

Step-by-step 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:

$sin(A)=\frac{Opposite}{Hypotenuse}\\sin(30)=\frac{x}{15}\\x=15*sin(30)=7.5$

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:

$cos(A)=\frac{Adjacent}{Hypotenuse}\\cos(60)=\frac{a}{7.5}\\a=7.5*cos(60)=3.75$

Thus $a=3.75$