Answer:
The tree is 37.5 ft tall.
Step-by-step explanation:
First, draw the tree and the ground and the line of the shadow forming a right triangle.
Draw a vertical segment on the left side of your paper about 1 inch long. Label the bottom point C and the top point A. Now from C draw a horizontal segment to the right about twice the length of vertical segment AC. Label the right endpoint of the new segment B. Now connect B and A. The vertical segment AC is the tree. Segment CB is the shadow cast by the tree on the ground. Angle C is a right angle, 90 deg. Angle B measures 32 deg. Segment CB has length 60 ft. Now we start with trigonometry.
Now we deal with triangle ABC. For the known angle B (given as 32 deg), side BC is the adjacent leg, side AC is the opposite leg, and side AB is the hypotenuse. We know the length of the shadow, which is adjacent leg BC, and it is 60 ft. We want to know side AC, which is the height of the tree and the opposite leg.
Known: measure of angle B = 32 deg
Known: adjacent leg BC = 60 ft
Find: length of opposite leg AC
The trig ratio that relates the opposite and adjacent legs is the tangent.
tan B = opp/adj
tan 32 = AC/60
AC = 60 * tan 32
AC = 37.5
Answer: The tree is 37.5 ft tall.
Answer:
y= -2x+ 3
Step-by-step explanation:
8 because all elements after nitrogen have not only two energy levels, they also find it easier to just get rid of electrons than to absorb electrons to get to 8 electrons.
Answer:
The equation of this line would be y = -1/2x + 1
Step-by-step explanation:
In order to find this equation we must first find the slope of the original line. To do this, we need to solve the original equation for y.
2x + 4y = 16
4y = -2x + 16
y = -1/2x + 4
The original slope (the coefficient of x) is -1/2, which means the new slope will also be -1/2 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line.
y - y1 = m(x - x1)
y - 2 = -1/2(x + 2)
y - 2 = -1/2x - 1
y = -1/2x + 1
Answer:
? = 45
Step-by-step explanation:
the inner and outer triangles are similar ( AA postulate )
Then the ratios of corresponding sides are in proportion, that is
= , that is
= ( divide numerator/denominator by 8 to simplify left side )
= ( cross- multiply )
7(105 + ? ) = 1050 ← distribute parenthesis on left side
735 + 7? = 1050 ( subtract 735 from both sides )
7? = 315 ( divide both sides by 7 )
? = 45