<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:
Step-by-step explanation:
(5/8)/(3+3/4)
(5/8)/(15/4)
(5/8)(4/15)
20/120
1/6
Answer:
V=144
Step-by-step explanation:
To find the volume of a pyramid, use the formula V=B•h, B being the base and h the height. So 12•12=144.
Answer:
should be pretty similar to how a parabola looks
Step-by-step explanation:
as the length increases the area gets huge fast
By definition we have:
A triangular pyramid (also called tetrahedron) is a polyhedron whose surface is formed by a base that is a triangle and triangular lateral faces that converge in a vertex that is called apex (or apex of the pyramid).
It will be composed, therefore, by 4 faces, the triangular base and three lateral triangles that converge at the vertex.
Thus, the surface area is:
As = 4 * (50.5) = 202 in ^ 2
Answer:
The total surface area of the triangular pyramid is:
202 in ^ 2