If in the triangle ABC , BF is an angle bisector and ∠ABF=41° then angle m∠BCE=8°.
Given that m∠ABF=41° and BF is an angle bisector.
We are required to find the angle m∠BCE if BF is an angle bisector.
Angle bisector basically divides an angle into two parts.
If BF is an angle bisector then ∠ABF=∠FBC by assuming that the angle is divided into two parts.
In this way ∠ABC=2*∠ABF
∠ABC=2*41
=82°
In ΔECB we got that ∠CEB=90° and ∠ABC=82° and we have to find ∠BCE.
∠BCE+∠CEB+EBC=180 (Sum of all the angles in a triangle is 180°)
∠BCE+90+82=180
∠BCE=180-172
∠BCE=8°
Hence if BF is an angle bisector then angle m∠BCE=8°.
Learn more about angles at brainly.com/question/25716982
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The answer is root. Hope this helps!
Answer:
x = 0.1, y = 0.075
Step-by-step explanation:
Given the 2 equations
27x + 24y = 4.5 → (1)
1.5x + y = 0.225 → (2)
Multiplying (2) by - 24 and adding to (1) will eliminate the y- term
- 36x - 24y = - 5.4 → (3)
Add (1) and (3) term by term to eliminate y
- 9x = - 0.9 ( divide both sides by - 9 )
x = 0.1
Substitute x = 0.1 into either of the 2 equations and solve for y
Substituting into (2)
1.5(0.1) + y = 0.225
0.15 + y = 0.225 ( subtract 0.15 from both sides )
y = 0.075
A right triangle has one leg with unknown length, the other leg with length of 5 m, and the hypotenuse with length 13 times sqrt 5 m.
We can use the Pythagorean formula to find the other leg of the right triangle.
a²+b²=c²
Where a and b are the legs of the triangle and c is the hypotenuse.
According to the given problem,
one leg: a= 5m and hypotenuse: c=13√5 m.
So, we can plug in these values in the above equation to get the value of unknown side:b. Hence,
5²+b²=(13√5)²
25 + b² = 13²*(√5)²
25 + b² = 169* 5
25+ b² = 845
25 + b² - 25 = 845 - 25
b² = 820
b =√ 820
b = √(4*205)
b = √4 *√205
b = 2√205
b= 2* 14.32
b = 28.64
So, b= 28.6 (Rounded to one decimal place)
Hence, the exact length of the unknown leg is 2√205m or 28.6 m (approximately).
