In triangle ABC, mc002-1.jpg is a right angle and mc002-2.jpg 45°
;. Find BC. If your answer is not an integer, leave it in simplest radical form.
Based on the given information, we have a right triangle ABC with angle C being 90 degrees and angle B being 45 degrees.
We know that the angles in a triangle add up to 180 degrees, so angle A is 180 - 90 - 45 = 45 degrees.
Since angle B and angle A are both 45 degrees, triangle ABC is an isosceles right triangle.
In an isosceles right triangle, the lengths of the two legs (AB and BC) are equal.
Let's assume the length of AB and BC is x.
Using the Pythagorean theorem, in a right triangle, the square of the hypotenuse (AC) is equal to the sum of the squares of the two legs.
AC^2 = AB^2 + BC^2
BC^2 = AC^2 - AB^2
= (x^2) - (x^2)
= 0
This means that if the length of AB is x, the length of BC is also x, which makes BC = x.
Therefore, the length of BC is equal to the length of AB, and since it is not given, we cannot determine the exact value of BC. We can only say that BC is also x, and this value is not an integer.
To find the length of BC in triangle ABC, we can use trigonometric ratios.
Since angle B is 45° and angle ABC is a right angle, angle ACB can be found by subtracting the sum of angles B and ABC from 180°:
ACB = 180° - (45° + 90°) = 45°.
Now we can use the tangent function to find BC:
tan(ACB) = BC / AB.
Since angle ACB is 45° and the opposite side is BC, and the adjacent side is AB, we have:
tan(45°) = BC / AB.
The tangent of 45° is equal to 1, so we have:
1 = BC / AB.
Rearranging the equation, we get:
BC = AB.
Therefore, the length of BC is equal to the length of AB.