Answer: scalene and obtuse
Justification:
You can find the angles using the law of cosine:
c^2 = a^2 + b^2 - 2abcos(γ)
=> cos(γ) = [a^2 + b^2 - c^2] / (2ab)
1) cos(γ) = [10^2 + 11^2 - 15^2] / (2*10*11) = - 0.0181818
=> γ = arccos(-0.0181818} ≈ 91°
2) cos(α) = [b^2 + c^2 - a^2 ] / 2bc = [11^2 + 15^2 - 10^2] / (2*11*15] = 0.7454545
=> α = arccos(0.7454545) ≈ 41.8°
3) cos(β) = [a^2 + c^2 - b^2] / (2ac) = [10^2 + 15^2 - 11^2] /(2*10*15) = 0.68
=> β = arccos(0.68) ≈ 47.2°
4) Verification: 91° + 41.8° + 47.2° = 180°
5) The triangles with the three different sides are called scalenes (which you can tell with only the measures of the sides).
6) The triangles with one angle greater than 90° are called obtuse.
So, the triangle is scalene and obtuse.
(-6)-(+8)-(-12)
-6-8+12
-14+12
-2
We are given
x1 = 10 ft
y1 = 14 ft
x2 = 13 ft
y2 = 9 ft
We are asked to find the distance between the base of the house to the closest treetop.
So,
d1 = √(10² + 14²) = 17.20
d2 √(13² + 9²) = 15.81
The distance is 15.81 ft to the closest treetop which is the tree 13 feet from the base of the house.
Answer:
Step-by-step explanation:
Because midpoints were used to make similar triangles we can say
AC=2(DE)
5x+12=2(9x-20)
5x+12=18x-40
-13x+12=-40
-13x=-52
x=4
AC=5x+12
AC=5(4)+12
AC=20+12
AC=32
