solve each triangle described below using Δ ABC :
1)a = 10, A = 16°, B = 49°
2)a = 8, b = 7, A = 88°
I don't know how to do this i forgot ... could u help (Steve, or Mrs.Sue, or Writeteacher plz help) this topic is Oblique triangle
I just did this one:
http://www.jiskha.com/display.cgi?id=1420462410
for #2.
using the sine law:
sinB/7 = sin88/8
sinB = 7sin88/8 = .8744...
angle B = 60.98° or angle B = 119.18° using the CAST rule
case1: B = 60.98, A = 88 , then C = 180-88-60.98 = 31.02°
or to the nearest angle:
A = 88 , B = 61, C = 31
Case2: B= 119, A =88 , then C = 180-119-88 = -27
But that would be "silly", so there is only the case1 answer.
thank you so much !! :)
Sure, I can help you solve oblique triangles. To solve these types of triangles, we usually use the Law of Sines or the Law of Cosines. Let's go step by step for each triangle:
1) Triangle with a = 10, A = 16°, B = 49°
First, let's label the triangle:
- Side opposite angle A is a;
- Side opposite angle B is b; and
- Side opposite angle C is c.
To solve this triangle, we need to find the remaining angles (C) and sides (b and c).
Step 1: Find angle C
Since the sum of the interior angles in a triangle is 180°, we can find angle C using the formula:
C = 180° - A - B
C = 180° - 16° - 49°
C = 115°
Step 2: Use the Law of Sines to find side b or c
The Law of Sines states that the ratio of a side length to the sine of its opposite angle is constant:
a/sin(A) = b/sin(B) = c/sin(C)
Let's use the known values to find side b:
10/sin(16°) = b/sin(49°)
Now, we can solve for b:
b = (10 * sin(49°)) / sin(16°)
b ≈ 11.67 (rounded to 2 decimal places)
Step 3: Find side c using the Law of Cosines
The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles:
c^2 = a^2 + b^2 - 2ab * cos(C)
Let's plug in the known values:
c^2 = 10^2 + 11.67^2 - 2 * 10 * 11.67 * cos(115°)
Now, we can solve for c:
c ≈ 5.47 (rounded to 2 decimal places)
Therefore, the sides of the triangle are: a = 10 units, b ≈ 11.67 units, and c ≈ 5.47 units.
2) Triangle with a = 8, b = 7, A = 88°
Again, let's label the triangle:
- Side opposite angle A is a;
- Side opposite angle B is b; and
- Side opposite angle C is c.
To solve this triangle, we need to find the remaining angles (B and C) and side c.
Step 1: Find angle B
Since the sum of the interior angles in a triangle is 180°, we can find angle B using the formula:
B = 180° - A - C
We don't have angle C yet, so we need to calculate it using the Law of Sines. Let's do that first.
Step 2: Use the Law of Sines to find angle C
We can find angle C using the formula:
sin(C) = (c * sin(A)) / a
Let's solve for C:
sin(C) = (c * sin(88°)) / 8
C = arcsin((c * sin(88°)) / 8)
Step 3: Find angle B
B = 180° - A - C
Now that we have C, we can solve for B:
B = 180° - 88° - C
Step 4: Find side c using the Law of Cosines
We can find side c using the formula:
c^2 = a^2 + b^2 - 2ab * cos(C)
Let's plug in the known values:
c^2 = 8^2 + 7^2 - 2 * 8 * 7 * cos(C)
Now, we can solve for c:
c ≈ 11.45 (rounded to 2 decimal places)
Therefore, the sides of the triangle are: a = 8 units, b = 7 units, and c ≈ 11.45 units.
I hope this explanation helps you solve oblique triangles in the future!