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2 years ago

13

Hello, how was your day, help? ^ ^ solve for x

1 answer:

Natali5045456 [20]2 years ago

6 0

Hi there!

»»————-　★　————-««

I believe your answer is:

$\boxed{x=100}$

»»————-　★　————-««

Here’s why:

Recall the Triangle Angle Sum Theorem: The three angles of all triangles add up to a sum of 180°.
We will set up an equation based on this and then solve.

⸻⸻⸻⸻

$\boxed{\text{Solve for 'x':}}\\\\58 + 22 + x = 180\\-----------\\\rightarrow 80 + x = 180\\\\\rightarrow 80 - 80 + x = 180 - 80\\\\\rightarrow \boxed{x=100}$

⸻⸻⸻⸻

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.

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If P is the orthocenter of △ABC, AB = 13, BF = 9,and FC = 5.6, find each measure & the perimeter of triangle ABC.

harina [27]

Answer:

$Perimeter = 38.6$

Step-by-step explanation:

Given

$A\ B = 13$

$B\ F = 9$

$F\ C = 5.6$

Required

Calculate the perimeter of A B C

To calculate the perimeter of A B C, we sum up the sides of the triangle

i.e.

$Perimeter = A B + B\ C + A\ C$

AB is given in the question already.

So, we need to calculate B F and F C

To solve for BF, we consider triangle B F C

Using Pythagoras Theorem, we have:

$B\ C^2 = B\ F^2 + F\ C^2$

Substitute values for BF and FC;

$B\ C^2 = 9^2 + 5.6^2$

$B\ C^2 = 81 + 31.36$

$B\ C^2 = 112.36$

$B\ C^2= \sqrt{112.36$

$B\ C = 10.6$

Next, we calculate A C.

To calculate A C, we need to calculate A F, considering triangle B F A

Using Pythagoras Theorem, we have:

$A\ B^2 = B\ F^2 + A\ F^2$

Substitute values for B F and A B;

$13^2 = 9^2 + A\ F^2$

$169= 81 + A\ F^2$

$A\ F^2 = 169 - 81$

$A\ F^2 = 88$

$A\ F = \sqrt{88$

$A\ F = 9.4$

Since F lies on line A C:

$A\ C = A\ F + F\ C$

$A\ C = 9.4 + 5.6$

$A\ C = 15.0$

Recall that:

$Perimeter = A\ B + B\ C + A\ C$

$Perimeter = 13 + 10.6 + 15.0$

$Perimeter = 38.6$

<em>Hence, the perimeter is 38.6</em>

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3 years ago