Answer:
1/4/2=1/8 1/4/3=1/12
"The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed."
<u>Answer:</u>
The quen is as following:
ABC is a right triangle at C,
Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1
If CH is an altitude to AB and CL is an angle bisector of ∠ACB, find m∠HCL.
<u>The solution is: m∠HCL = 30°</u>
<u>Step-by-step explanation:</u>
See the attached figure.
∵The triangle is right at C ∴∠C = 90°
∴∠A + ∠B = 90° ⇒(1)
∵ Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1
∴∠A = 5 times ∠B
Substitute at (1)
∴ 5 ∠B + ∠B = 90° ⇒⇒⇒ ∴∠B = 15° and ∠A = 75°
∵CL is an angle bisector of ∠ACB
∴ ∠ACL = 90°/2 = 45°
∵ CH is an altitude to AB ⇒ ∠CHA = 90°
At the triangle AHC:
∠ACH = 180° - (∠CHA + ∠CAH) = 180° - (90° + 75°) = 15°
<u>∴ ∠HCL = ∠ACL - ∠ACH = 45° - 15° = 30°</u>