In the isosceles △ABC m∠ACB=120° and AD is an altitude to leg BC . What is the distance from D to base AB , if CD=4cm?
2 answers:
If ΔACB is an isosceles triangle, then ∠A ≅ ∠B and AC ≅ CB
Since ∠C = 120° and ∠A + ∠B + ∠C = 180°, then ∠A = 30° and ∠B = 30°
Next, look at ΔADB. ∠A + ∠D + ∠B = 180°, so ∠A + 90° + 30° = 180° ⇒ ∠A = 30°
Now look at ΔADC. Since ∠A = 30° in ΔACB, and ∠A = 60° in ΔADB, then ∠A = 30° in ΔADC <em>per angle addition postulate.</em>
Now that we have shown that ΔADB and ΔADC are 30-60-90 triangles, we can use that formula to calculate the side lengths.
CD = 4 cm (given) so AC = 2(4 cm) = 8 cm
Since AC ≅ BC, then BC = 8 cm. Therefore, BD = 4 + 8 = 12 <em>by segment addition postulate.</em>
Lastly, look at ΔBHD. Since ∠B = 30° and ∠H = 90°, then ∠D = 60°. So, ΔBHD is also a 30-60-90 triangle.
BD = 12 cm, so HD = = 6 cm
Answer: 6 cm
You might be interested in
Answer: (0.066,0.116)
Step-by-step explanation:
The confidence interval for proportion is given by :-
Given : The proportion of men have red/green color blindness =
The proportion of women have red/green color blindness =
Significance level :
Critical value :
Now, the 99% confidence interval for the difference between the color blindness rates of men and women will be:-
Hence, the 99% confidence interval for the difference between the color blindness rates of men and women= (0.066,0.116)
Answer:
- First, you want to divide the numerator and denominator by the cosine(x), and afterwards, it looks like this...
- Include 45 as one of the parameters and correlate with <em>tan</em>.
- Next, you want to multiply the numerator and denominator by the conjugate of the denominator, in this case, <em>tan x + tan 45.</em>
- Lastly, simplify, and you have the answer as <em>tan(45 + x)</em>