In isosceles triangle ACB, AB=AC =4cm,BAC=30 and CN is an altitude. Find BN
Please I need the diagram
Sorry, as an AI language model, I cannot produce images.
Draw 2 arms AB and AC which form an angle of 30°. Join BC
draw a line from A to BC, to meet BC at N at 90°
look at triangle ABN,
cos 15° = BN/4
BN = 4sin15° = appr 1.035
so BC = 2(1.035..) = appr 2.07
or
you could use the cosine law
BC^2 = 4^2 + 4^2 - 2(4)(4)cos30 = 4.28718..
BC = √4.28718.. = appr 2.07 , same as before
Thank you for providing the explanation and calculations!
Sure, here is the diagram of the given isosceles triangle ACB with AB = AC = 4cm and BAC = 30 degrees.
```
C
/|\
/ | \
/ | \
A----N----B
```
To find BN, we need to use the properties of an isosceles triangle and the definition of altitude.
Since AB = AC, triangle ACB is an isosceles triangle, which means that angles BAC and BCA are congruent. Therefore, angle BCA is also 30 degrees.
We are given that CN is an altitude, which means it is perpendicular to AB.
Now, let's consider the right triangle BNC. The right angle is at point N, and the length of the hypotenuse BC is 4cm.
Since angle BCA is 30 degrees and angle BNC is 90 degrees, we can use trigonometric ratios to find BN.
Using the trigonometric ratio for the sine of an angle, which is the opposite side divided by the hypotenuse, we have:
sin(30) = BN / BC
Substituting the known values, we have:
sin(30) = BN / 4
To find BN, we can solve this equation for BN:
BN = 4 * sin(30)
Using a calculator, we find:
BN ≈ 2 cm
Therefore, BN is approximately 2 cm.