Answer:
29 × 51 inches
Step-by-step explanation:
If the scale is ...
photo : painting = 1 : 3
then each dimension of the painting is 3 times the corresponding dimension of the photo. The painting is (3×13) by (3×17) inches, or 39 × 51 inches.
Answer:
ZA = 3 cm
Step-by-step explanation:
Point A is the incenter of the triangle, so segments AX, AY, and AZ are radii of the circle. They are all the same length, given as 3 cm and confirmed by 3-4-5 right triangle AYD.
ZA = 3 cm
Answer:
The Figure for Right triangle is below,
Therefore , 15 unit length represents BC.
Step-by-step explanation:
Given:
Consider a right triangle ABC, Such that
To Find:
BC = ?
Solution:
In Right Angle Triangle ABC, Cosine and Tangent identity
BUT,
....Given
On Comparing,
Adjacent side to angle A = AB = 15
Opposite side to angle A = BC = 8
Hypotenuse = AC =17
Also Pythagoras theorem is Satisfies,
The Figure for Right triangle is below,
Therefore , 15 unit length represents BC.
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Tan ( A - B ) = ( tan A - tan B ) / ( 1 + tan A tan B )
tan A = 3 tan B/2
tan ( A - B ) = ((3 tan B/ 2)-tan B) / ( 1 + 3 tan² B/2)=
= (tan B/2) / ( 2 + 3 sin²B/cos²B )=
= (sin B / cos B) / (( 2cos² B+3sin²B)/cos²B)=
=( sin B cos B ) / ( 2 cos²B + 3 ( 1 - cos² B ) ) =
= (sin B cos B ) / ( 2 cos² B + 3 - 3 cos² B ) =
= ( sin 2 B ) / 2 ( 3 - cos² B ) =
= ( sin 2 B ) / ( 6 - cos² B )=
= ( sin 2 B ) / ( 5 + 1 - 2 cos² B )=
= ( sin 2 B ) / ( 5 + sin² B + cos ² B - 2 cos² B ) =
= ( sin 2 B ) / ( 5 - ( cos² B - sin² B ) ) =
= ( sin 2 B ) / ( 5 - cos 2 B ) - correct
