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Andreyy89
3 years ago
5

Need help fast plz for my pre calc exam

Mathematics
1 answer:
bezimeni [28]3 years ago
6 0

Answer:

<em>h = 8.54 units</em>

Step-by-step explanation:

<u>The Law of Cosines </u>

It relates the length of the sides of a triangle with one of its internal angles.

Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:

c^2=a^2+b^2-2ab\cos x

Since we know the values of all three side lengths, we solve the equation for x:

\displaystyle \cos x=\frac{a^2+b^2-c^2}{2ab}

For the triangle ABC in the image, a=10, b=15, c=13, thus:

\displaystyle \cos A=\frac{10^2+15^2-13^2}{2*10*15}

\displaystyle \cos A=\frac{156}{300}

\displaystyle \cos A=0.52

Thus, A = 58.67°

For the right triangle of height h and hypotenuse 10, we use the sine ratio:

\displaystyle \sin 58.67^\circ=\frac{h}{10}

Solving for h:

h = 10\sin 58.67^\circ

h = 8.54 units

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