Answer:
It is incorrect because the following gives you a total of 171 and not 1.
Step-by-step explanation:
Answer:
u=4
v=2√3
Step-by-step explanation:
The 30-60-90 triangle theorem states that the shortest side of a triangle is half of the hypotenuse, so 2*2=4. So, the hypotenuse, <em>u</em>, is 4.
The longest leg is √3 times greater than the shortest leg, so 2*√3=2√3. So, the longest leg, <em>v</em>, is 2√3.
Answer:
<h2>3.6°</h2>
Step-by-step explanation:
The question is incomplete. Here is the complete question.
Find the angle between the given vectors to the nearest tenth of a degree.
u = <8, 7>, v = <9, 7>
we will be using the formula below to calculate the angle between the two vectors;
![u*v = |u||v| cos \theta](https://tex.z-dn.net/?f=u%2Av%20%3D%20%7Cu%7C%7Cv%7C%20cos%20%5Ctheta)
is the angle between the two vectors.
u = 8i + 7j and v = 9i+7j
u*v = (8i + 7j )*(9i + 7j )
u*v = 8(9) + 7(7)
u*v = 72+49
u*v = 121
|u| = √8²+7²
|u| = √64+49
|u| = √113
|v| = √9²+7²
|v| = √81+49
|v| = √130
Substituting the values into the formula;
121= √113*√130 cos θ
cos θ = 121/121.20
cos θ = 0.998
θ = cos⁻¹0.998
θ = 3.6° (to nearest tenth)
Hence, the angle between the given vectors is 3.6°
0.319 rounded to the nearest hundredths is 0.32. Because 9 is over 5 which makes it round up.
The triangle has a 45-deg angle.
The base angles are congruent and measure 67.5 deg.
The congruent sides measure 1 ft.
Use law of sines to find the length of the base.
![\dfrac{\sin 67.5^\circ}{1~ft} = \dfrac{\sin 45^\circ}{b}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B%5Csin%2067.5%5E%5Ccirc%7D%7B1~ft%7D%20%3D%20%5Cdfrac%7B%5Csin%2045%5E%5Ccirc%7D%7Bb%7D%20)
![b = \dfrac{\sin 45^\circ}{\sin 67.5^\circ}~ft](https://tex.z-dn.net/?f=%20b%20%3D%20%5Cdfrac%7B%5Csin%2045%5E%5Ccirc%7D%7B%5Csin%2067.5%5E%5Ccirc%7D~ft%20)
![b = 0.765~ft](https://tex.z-dn.net/?f=%20b%20%3D%200.765~ft%20)
Draw a height from the vertex of the 45-deg angle to the base.
Half of the base is 0.765 ft/2 = 0.383 ft
We can find the height of the triangle using the small triangles.
0.383^2 + h^2 = 1^2
h = 0.9239 ft
A = bh/2 = 0.765 * 0.9239/2 ft^2
A = 0.354 ft^2