Download Question #56860, Math / Geometry 1. The ratio of the base of an

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Transcript
Question #56860, Math / Geometry
1. The ratio of the base of an isosceles triangle to its altitude is 3:4. Find the
measures of the angles of the triangle.
2. Two altitudes of an isosceles triangle are equal to 20 cm and 30 cm. Determine
the possible measures of the base angles of the triangle.
3. The area of a triangle is equal to 48cm^2 and two of its sides measure 12 cm
and 9 cm, respectively. Find the possible measures of the included angles of the
given sides.
Answer.
1.
𝑨𝑩
𝑪𝑫
=
𝟑
𝟒
→ 𝒕𝒂𝒏⦟𝑨 = 𝒕𝒂𝒏⦟𝑩 =
⦟𝑨 = ⦟𝑩 = 𝒂𝒓𝒄𝒕𝒂𝒏
𝑪𝑫
𝑨𝑩
𝟐
=
𝟖
𝟑
→
𝟖
≈ 𝟔𝟗. 𝟒𝟒𝟎 , ⦟𝑪 = 𝟏𝟖𝟎𝟎 − 𝟐 ∗ 𝟔𝟗. 𝟒𝟒𝟎 = 𝟒𝟏. 𝟏𝟐𝟎
𝟑
2.
𝑪𝑫 = 𝟑𝟎, 𝑨𝑬 = 𝟐𝟎.
𝑨𝑩
𝑩𝑪𝑫~𝑨𝑩𝑬 →
𝑪𝑩
=
→ ⦟𝑩 = ⦟𝑨 = 𝒂𝒓𝒄𝒄𝒐𝒔
𝑨𝑬
𝑪𝑫
𝑩𝑫
𝑪𝑩
=
𝟐𝟎
𝟑𝟎
=
𝟐
𝟑
𝟐
𝟏
𝟑
𝟑
→ 𝑨𝑩 = 𝑪𝑩 → 𝑩𝑫 = 𝑪𝑩 →
𝟏
= 𝒂𝒓𝒄𝒄𝒐𝒔 ( ) ≈ 𝟕𝟎. 𝟓𝟑𝟎
𝟑
𝟏
𝟏
𝟒𝟖
𝟐
𝟐
𝟓𝟒
3. 𝑺 = 𝒂𝒉 = 𝟏𝟐 ∗ 𝟗𝒔𝒊𝒏𝜶 = 𝟒𝟖 → 𝒔𝒊𝒏𝜶 =
=
𝟖
𝟗
→
𝟖
→ 𝜶 = 𝒂𝒓𝒄𝒔𝒊𝒏 ( ) ≈ 𝟔𝟐. 𝟕𝟑𝟎
𝟗
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