Angle of elevation is 15 degrees and we're trying to solve for the hypotenuse of the right triangle given the adjacent is 7.11 m.

We could use primary trig ratios to solve - COS.

Let x represent the length of the ramp (hypotenuse)

Cos15= ADJACENT/HYPOTENUSE
Cos15= 7.11/x
x=7.11/cos15
x=7.36 m

<span>Therefore, the ramp is 7.36 m in length.

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5 0

4 years ago

Given vectors u = ⟨2, –3⟩ and v = ⟨1, –1⟩, what is the measure of the angle between the vectors?

oksano4ka [1.4K]

Answer:

The measure of the angle between the vectors = Ф = 11.30°

Step-by-step explanation:

Given

u = ⟨2, –3⟩

v = ⟨1, –1⟩

$\mathrm{Computing\:the\:angle\:between\:the\:vectors}:\quad \cos \left(\theta \right)\:=\frac{\vec{a\:}\cdot \vec{b\:}}{\left|\vec{a\:}\right|\cdot \left|\vec{b\:}\right|}$

Next, find the lengths of the vectors:

$\mathrm{Computing\:the\:Euclidean\:Length\:of\:a\:vector}:\quad \left|\left(x_1\:,\:\:\ldots \:,\:\:x_n\right)\right|=\sqrt{\sum _{i=1}^n\left|x_i\right|^2}$

u = ⟨2, –3⟩

$\:\:\left|u\right|\:=\sqrt{2^2+\left(-3\right)^2}$

$=\sqrt{13}$

u = ⟨2, –3⟩

$|v|=\sqrt{1^2+\left(-1\right)^2}$

$=\sqrt{2}$

Finally, the angle is given by:

$\mathrm{Computing\:the\:angle\:between\:the\:vectors}:\quad \cos \left(\theta \right)\:=\frac{\vec{a\:}\cdot \vec{b\:}}{\left|\vec{a\:}\right|\cdot \left|\vec{b\:}\right|}$

cos (Ф) = 5/√26

Ф = arc cos (cos (Ф)) = arc cos (5 √26) / (26)

Ф = 11.30°

Thus, the measure of the angle between the vectors = Ф = 11.30°

6 0

3 years ago

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