Gavyn Whitehead
2022-09-12
Answered

The lines containing the bisectors of the exterior angles at vertices B and C of triangle ABC intersect at point O. find angle BOC if angle A is equal to $$\alpha $$.

You can still ask an expert for help

Aubrie Conley

Answered 2022-09-13
Author has **13** answers

In the triangle ABC, the interior angles are: $$\mathrm{\angle}A=a,\mathrm{\angle}B=x,\mathrm{\angle}C=180-a-x$$.

External corners: in $$\mathrm{\angle}B=180-x$$ and in $$\mathrm{\angle}C=a+x$$.

In a triangle BOC, by condition, the angles are equal:

$$\mathrm{\angle}OBC=in\mathrm{\angle}B/2=(180-x)/2=90-x/2;$$

$$\mathrm{\angle}OCB=in\mathrm{\angle}C/2=(a+x)/2=a/2+x/2.$$

Then $$\mathrm{\angle}BOC=180-\mathrm{\angle}BOC-\mathrm{\angle}OCB=180-(90-x/2)-(a/2+x/2)=90-a/2$$

External corners: in $$\mathrm{\angle}B=180-x$$ and in $$\mathrm{\angle}C=a+x$$.

In a triangle BOC, by condition, the angles are equal:

$$\mathrm{\angle}OBC=in\mathrm{\angle}B/2=(180-x)/2=90-x/2;$$

$$\mathrm{\angle}OCB=in\mathrm{\angle}C/2=(a+x)/2=a/2+x/2.$$

Then $$\mathrm{\angle}BOC=180-\mathrm{\angle}BOC-\mathrm{\angle}OCB=180-(90-x/2)-(a/2+x/2)=90-a/2$$

asked 2021-05-31

Find an equation of the plane. The plane through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1)

asked 2021-05-19

Find the point on the line

asked 2020-11-26

Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter(A,B, C, D or E)in each blank

A .$\mathrm{tan}\left(\mathrm{arcsin}\left(\frac{x}{8}\right)\right)$

B .$\mathrm{cos}\left(ar\mathrm{sin}\left(\frac{x}{8}\right)\right)$

C.$\left(\frac{1}{2}\right)\mathrm{sin}\left(2\mathrm{arcsin}\left(\frac{x}{8}\right)\right)$

D.$\mathrm{sin}\left(\mathrm{arctan}\left(\frac{x}{8}\right)\right)$

E.$\mathrm{cos}\left(\mathrm{arctan}\left(\frac{x}{8}\right)\right)$

A .

B .

C.

D.

E.

asked 2020-11-26

Calculate the tension

asked 2022-08-08

There is a rectagular room with the sides 6m x 4m. The height is 3m.

Find the distance from a corner of the floor to the opposide corner on the ceiling.

Find the distance from a corner of the floor to the opposide corner on the ceiling.

asked 2021-03-02

Is this triangle a right triangle

asked 2021-02-09

what is the length of the hypotenuse of a right triangle with legs of length 7 and 8