Answer:
17.7 cm^2
Step-by-step explanation:
Use trig to find the height of the triangle. Then the area is bh/2.
Extend side BC to the right until it is vertically below point A. Draw a segment from point A vertically down until it intersects the extension of side BC. Call the point of intersection D. <D is a right angle.
Use triangle ABD to find the height, AD, of triangle ABC.
For <B of 37 deg, AD is the opposite leg. AB is the hypotenuse. The trig ratio that relates the opposite lefg to the hypotenuse is the sine.
sin B = opp/hyp
sin 37 deg = AD/13.1
AD = 13.1 * sin 37 deg
AD = 7.9
AD is the height of triangle ABC. BC is the base. We can find the area of triangle ABC.
area = bh/2
area = (4.5 cm)(7.9 cm)/2
area = 17.7 cm^2
Using the dot product:
For any vector x, we have
||x|| = √(x • x)
This means that
||w|| = √(w • w)
… = √((u + z) • (u + z))
… = √((u • u) + (u • z) + (z • u) + (z • z))
… = √(||u||² + 2 (u • z) + ||z||²)
We have
u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37
z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74
u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46
and so
||w|| = √((2√37)² + 2•46 + (√74)²)
… = √(4•37 + 2•46 + 74)
… = √314 ≈ 17.720
Alternatively, without mentioning the dot product,
w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩
and so
||w|| = √((-5)² + 17²) = √314 ≈ 17.720
Answer:
x intercept= (-3,0) y intercept= (0,3)
Step-by-step explanation:
for x intercepts, y should equal zero
for y intercepts, x should equal zero
x intercept: -x+0=3
-x=3
x=-3 (x,y)--> (-3,0)
y intercept: 0+y=3
y=3 (x,y)--> (0,3)
