<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>
Answer:
d
Step-by-step explanation: cause thats the only answer that will maked sense
Answer:
I did the first one
Step-by-step explanation:
Hope I did it right
Answer:
Step-by-step explanation:
1.5 quarts of grape juice should be mixed with 3/4 quarts of water.
1.5 is the same as 3/2. Our ratio is 3/2 : 3/4
If we multiply everything by 4, things will get even easier to understand.
This gives us a ratio of (4 x 3/2) : (4 x 3/4)...
...or more simply put as 6 : 3
Which is even more simply put as 2:1
so for 15/4 we want
15/4 x 2 = 15/2
or 7.5 quarts if you want to express it once again as a decimal.
(We can also attack the problem by simply considering is all in decimals at the outset; 1.5 quarts grape mixed with 0.75 quarts of water. The 2: 1 relationship is quite obvious looking at this. Once again 15/4 x 2 = 15/2 or seven and a half quarts).
Actual selling price: $7.35
Markdown: $2.65
10-2.65= 7.35