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tatiyna
3 years ago
15

Find missing part Answer started below x=

Mathematics
2 answers:
MArishka [77]3 years ago
8 0

Answer:

x=7.5

Step-by-step explanation:

If you look at the large triangle, you will see that the side x is opposite of 30° angle and the side 15 is opposite of 90° angle (<em>side opposite of 90° angle is called the hypotenuse</em>).

We have the angle, we have the side opposite and the hypotenuse. Which trigonometric ratio relates opposite side and hypotenuse? SINE!

<em>So we use the sin ratio and cross multiply and solve for x:</em>

Sin(A)=\frac{Opposite}{Hypotenuse}\\Sin(30)=\frac{x}{15}\\x=15*Sin(30)\\x=15*(0.5)\\x=7.5

Hence, x=7.5

uysha [10]3 years ago
7 0

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.



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