Common Tangents and AAA theorems
1 answer:
You know from similar triangles that ...
KM/KO = LM/LN
(20 +x)/12 = x/8
Multiplying by 24, we get
2(20 +x) = 3x
40 +2x = 3x
Subtracting 2x, we get
40 = x . . . . . . . . . . the measure of LM
The Pythagorean theorem tells us
(LN)² +(NM)² = (LM)²
Substituting known values, this becomes
8² +(NM)² = 40²
(NM)² = 40² -8² = 1600 -64 = 1536
Then the measure of NM is ...
NM = √1536 ≈ 39.19
KM/KO = LM/LN
(20 +x)/12 = x/8
Multiplying by 24, we get
2(20 +x) = 3x
40 +2x = 3x
Subtracting 2x, we get
40 = x . . . . . . . . . . the measure of LM
The Pythagorean theorem tells us
(LN)² +(NM)² = (LM)²
Substituting known values, this becomes
8² +(NM)² = 40²
(NM)² = 40² -8² = 1600 -64 = 1536
Then the measure of NM is ...
NM = √1536 ≈ 39.19
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Answer:
Step-by-step explanation:
The submersible is diving at a down angle of 15° along the hypotenuse AC of triangle ABC.
Its horizontal track along the surface AB is 1500 ft.
The submersible was already at a depth of 250 feet when it began the dive.
New depth = 250 + 402 = 652 ft
Answer:
9 yd
Step-by-step explanation:
A cube consists of 6 square faces.
Divide the surface area by 6 for the area of one face
486 ÷ 6 = 81 yd²
The area of a square is
A = s² ( s is the side length )
Here A = 81, then
s² = 81 ( take the square root of both sides )
s = = 9
Thus side length is 9 yd