1. Give the measure of the other acute angle of right ⊿ACB.
A=45°,B= _____
B=25°,A= _____
A=24°10', B=_____
B=26°26', A=_____
A=58°,B= _____
2. Give the measure of the other side of the right ⊿ACB.
a=3,b=4,c= _____
c=13,a=5,b= _____
b=12,c=15,a=_____
a=7,b=24,c= _____
c=29,a=20,b=_____
Answers
Answer:
1.
A=45°,B= 45°
B=25°,A= 65°
A=24°10', B= 65°90'
B=26°26', A= 63°64'
A=58°,B= 32°
given : ⊿ACB is right triangle.
so, angle (A + B + C) = 180° [ASP]
[angle C = 90°]
angle[A + B] = 90°
by substituting the value of angle A or B we can find other angle.
2.
a=3,b=4,c = 5
c=13,a=5,b= 12
b=12,c=15,a=9
a=7,b=24,c= 25
c=29,a=20,b=21
given : ⊿ACB is right triangle.
we can find the values using Pythagoras theorem.
H² = P² + B²
In ⊿ACB ,
H = c
B = b
P = a
substitute the values and you will get the answer.
Answer:
search-icon-header
Search for questions & chapters
search-icon-image
Question
Bookmark
ABC is a right-angled triangle, right-angled at B/. Given that ∠ACB=θ, side AB=2 units and side BC=1 unit, find the value of sin
2
θ+tan
2
θ.
1140973
expand
Medium
Solution
verified
Verified by Toppr
sinθ=
AB
2
AC
;tanθ=
BC
AC
⎣
⎢
⎢
⎡
∵AB=
5
AC=2
BC=1
⎦
⎥
⎥
⎤
In △ABC,∠B=90
o
By Pythagoras theorem,
∴sinθ=
AB
AC
sinθ=
5
2
tanθ=
1
2
AB
2
=AC
2
+BC
2
AB
2
=2
2
+1
2
AB=
5
∴sin
2
θ+tan
2
θ=(
5
2
)
2
+(
1
2
)
2
=
5
4
+
2
4
=
5
4+4×5
=
5
24