Please answer this in two minutes

Mathematics

1 answer:

Margarita [4]3 years ago

4 0

Answer:

$t = 17.3$

Step-by-step explanation:

Given:

∆TUV,

m < T = 87°

VT = u = 11

TU = v = 14

VU = t = ?

Use the Law of Cosines to find t as shown below:

$t^2 = u^2 + v^2 - 2uv*cos(T)$

$t^2 = 11^2 + 14^2 - 2*11*14*cos(87)$

$t^2 = 121 + 196 - 308*0.0523$

$t^2 = 317 - 16.1084$

$t^2 = 300.89$

$t = 17.3$ (rounded to the nearest tenth)

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List the sides of triangle ΔMNP in ascending order (shortest to longest) if: Chapter Reference a m∠M = 64°, m∠N = 48°

scoray [572]

The given angles are
M = 64
N = 48
where P is unknown. While we don't know P at first, we can solve for it. Recall that for any triangle, the three angles always add to 180 degrees

M+N+P = 180
64+48+P = 180
112+P = 180
112+P-112 = 180-112
P = 68

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So in summary so far
M = 64
N = 48
P = 68

The shortest side is opposite the smallest angle. The side MP is opposite the smallest angle N = 48

The longest side is going to be opposite the largest angle. In this case, side MN is opposite the largest angle P = 68

The medium side is opposite the medium angle. So NP is the medium side length

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Final Answers:
Shortest Side = MP
Medium Side = NP
Longest Side = MN
See the attached image for a visual summary

The ascending order would be: MP, NP, MN

Note: Something like MP is the same as PM. The order of endpoints for any given individual segment doesn't matter