Answer:
The measure of angle F is 67.6°
Step-by-step explanation:
In the right triangle DEF
∵ ∠E is the right angle
∵ Side DF is opposite to ∠E
∴ DF is the hypotenuse of the triangle DEF
∵ Side EF is the adjacent side of ∠F
∵ The cosine ratio = ![\frac{Adjacent}{Hypotenuse}](https://tex.z-dn.net/?f=%5Cfrac%7BAdjacent%7D%7BHypotenuse%7D)
∴ cos∠F = ![\frac{EF}{DF}](https://tex.z-dn.net/?f=%5Cfrac%7BEF%7D%7BDF%7D)
∵ EF = 8 units
∵ DF = 21 units
→ Substitute them in the cosine ratio above
∴ cos∠F = ![\frac{8}{21}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B21%7D)
→ Use
to find the measure of angle F
∵ m∠F = ![cos^{-1}(\frac{8}{21})](https://tex.z-dn.net/?f=cos%5E%7B-1%7D%28%5Cfrac%7B8%7D%7B21%7D%29)
∴ m∠F = 67.60731219 degrees
→ Round it the nearest tenth of a degree
∴ m∠F = 67.6°
∴ The measure of angle F is 67.6°
Answer: y= -7 y= -5 y= -3 y= -1
Step-by-step explanation:
By doing the addends of 4+5 :)
Answer:
The value of BD is 6√3 cm and BF = 3√3 cm.
Explanation:
Firstly, we have to find the length of BD using Tangent Rule, tanθ = oppo./adj. :
θ = 60°
adj. = 6 cm
oppo. = BD
tan 60° = BD/6
BD = 6 tan 60°
= 6√3 cm
Next, we have to find the length of BF but we have to find the angle of BAF first. In order to find the angle of BAF, we have to substract ∠ACE and ∠AEC from 180° as the total interior angle for triangle is 180° :
∠CAE + ∠ACE + ∠AEC = 180°
∠CAE + 60° + 90° = 180°
∠CAE = 180° - 90° - 60°
= 30°
∠BAF = ∠CAE = 30°
θ = 30°
oppo. = BF
adj. = 9 cm
tan 30° = BF/9
BF = 9 tan 30°
= 3√3 cm
Answer:
P=77, Q=60
Step-by-step explanation:
Angle BCA is 180-137=43. BCA and YAC are opposite interior angles, which are congruent, so YAC is also 43.
To find P, you just take 60+P+43=180 (straight line). So, P should be 77.
You can figure out Q by using the total degrees in a triangle, 180. You have the other two angles now (43 and 77), so Q is 180-43-77=60. Incidentally, this is also the opposite interior angle of XAB, which is equivalent to Q at 60.