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3 years ago

Find x in this triangle

Mathematics

2 answers:

Elodia [21]3 years ago

8 0

The angle between the 35 and 60 degree angles equals:180 -35 -60 = 85 degreesThis makes the angle next to the "x" angle = 5 degrees.So, angle "x" equals 180 -5 = 175 degrees.

tamaranim1 [39]3 years ago

8 0

Hi,
The angle of 60° is an outside angle of a triangle (equal the sum of the others angles of the triangle : in french un angle extérieur d'un triangle)

If x is inside the triangle:
60°=35°+x==>x=25°

If x is outside the triangle:
x=180°-25°=155°

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3 years ago

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Geometry Question attached below

Soloha48 [4]

I'm sure there's an easier way to do this, but this method does work:

First, AB = CD = CG + GF + FD, so FG = 2.

By the Pythagorean theorem, in triangle AFD we get

$1^2+3^2=A F^2\implies A F=\sqrt{10}$

and in triangle BCG,

$2^2+3^2=BG^2\implies BG=\sqrt{13}$

Angles AFD and EFG form a vertical pair, so they are congruent and have measure

$m\angle EFG=\tan^{-1}3$

Similarly, angles BGC and FGE are congruent and have measure

$m\angle FGE=\tan^{-1}\dfrac32$

Then the remaining angle in triangle EFG has measure

$m\angle FEG=\pi-\tan^{-1}3-\tan^{-1}\dfrac32$

We can solve for the lengths of FE and GE exactly by applying the law of sines:

$\dfrac{\sin\left(\pi-\tan^{-1}3-\tan^{-1}\frac 32\right)}2=\dfrac{\sin\left(\tan^{-1}3\right)}{GE}=\dfrac{\sin\left(\tan^{-1}\frac32\right)}{FE}$

$\implies GE=\dfrac{2\sqrt{13}}3,FE=\dfrac{2\sqrt{10}}3$

Let $s$ be the semiperimeter of triangle ABE, so that

$s=\dfrac{AB+BE+EA}2$

Then according to Heron's formula, the area of triangle ABE is

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4 years ago

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Answer:

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Step-by-step explanation:

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So, it took 11 weeks for the factory to be at half capacity.

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3 years ago

from a point on the ground 12ft from the base of a flagpole, the angle of elevation of the top of the pole measures 53 degrees.

krek1111 [17]

Answer: the flagpole is 16 feet tall.

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