Answer:
The measurement of angle HBC is m∠HBC=61°
Step-by-step explanation:
The given problem states that
The line BH divides angle EBC into two equal parts,
consult the attached diagram for clarity
thus
m∠EBC=m∠EBH+m∠HBC
where m∠EBH=m∠HBC
therefore
m∠EBC=2(m∠EBH)
Insert the provided values to solve for a
Determine the value of angle EBH
m∠EBH=(4(4)+45)=61°
Keep in mind that
m∠EBH=m∠HBC
therefore
The measurement of angle HBC is m∠HBC=61°
Indeed, a fare of $40 is a fair charge for the cab ride.
Explanation
Sheri's cab fare totaled $32, with a gratuity rate of 20%.
The gratuity amount is:
Thus, the total cab fare including gratuity is:
Since Sheri issued a $40 check to the cab driver, it indicates she provided ($40 - $38.40) or an extra $1.60 to the cab driver. Consequently, the $40 payment is reasonable for the cab fare.
Response:
Step-by-step breakdown:
When you sketch that diagram (great description, by the way!), what you essentially have is a right triangle with a base of 32 and a hypotenuse of 45. The right angle resides at one of the base's ends, and x represents the vertex angle. We must find this vertex angle first to determine the angle of depression from the second bird to the watcher. The side measuring 32 is opposite to angle x, with 45 being the hypotenuse; hence, the trigonometric relation we need is sine:
and
sin(x) =.711111111
Go to your calculator, press the 2nd key followed by the sin key, and your display will show:
then, enter in your decimal.711111111 and hit equals. You should arrive at an angle of 45.325. That angle is x. However, that's not the angle of depression. The angle of depression is the complementary angle to x.
Angle of depression = 90 - angle x and
Angle of depression = 90 - 45.325, resulting in
Angle of depression = 44.67 or 44.7 degrees.